Semantic Graph — Visual Examination Report

{
  "nodes": [
    {
      "id": "__multiply_1",
      "type": "operator",
      "op": "multiply",
      "subexpr": "\\langle \\phi | \\hat{A} | \\psi \\rangle",
      "chartScript": {
        "script": "A*hat*<phi|psi>",
        "variables": [
          "A",
          "hat",
          "phi",
          "psi"
        ]
      }
    },
    {
      "id": "__bra_2",
      "type": "bra",
      "latex": "\\left\\langle \\phi\\right|",
      "subexpr": "\\left\\langle \\phi\\right|",
      "chartScript": {
        "script": "<phi|",
        "variables": [
          "phi"
        ]
      }
    },
    {
      "id": "__multiply_3",
      "type": "operator",
      "op": "multiply",
      "subexpr": "\\hat{A} {\\left|\\psi\\right\\rangle }",
      "chartScript": {
        "script": "A*hat*|psi>",
        "variables": [
          "A",
          "hat",
          "psi"
        ]
      }
    },
    {
      "id": "A",
      "type": "scalar",
      "latex": "\\hat{A}",
      "subexpr": "\\hat{A}",
      "chartScript": {
        "script": "A*hat",
        "variables": [
          "A",
          "hat"
        ]
      }
    },
    {
      "id": "__ket_4",
      "type": "ket",
      "latex": "\\left|\\psi\\right\\rangle",
      "subexpr": "\\left|\\psi\\right\\rangle",
      "chartScript": {
        "script": "|psi>",
        "variables": [
          "psi"
        ]
      }
    }
  ],
  "edges": [
    {
      "from": "__bra_2",
      "to": "__multiply_1",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "A",
      "to": "__multiply_3",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "__ket_4",
      "to": "__multiply_3",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "__multiply_3",
      "to": "__multiply_1",
      "semantic": "direct",
      "weight": 1.0
    }
  ],
  "classification": {
    "kind": "algebraic"
  },
  "domain": "quantum_mechanics"
}

flowchart RL
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  classDef vector fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef constant fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
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  classDef expression fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
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  classDef operator fill:#1a2740,stroke:#42a5f5,color:#bbdefb,font-size:15px
  classDef function fill:#1a2740,stroke:#42a5f5,color:#bbdefb,font-size:15px
  classDef relation fill:#332a0b,stroke:#ffa726,color:#ffe0b2,font-size:15px
  classDef result fill:#332a0b,stroke:#ffa726,color:#ffe0b2,font-size:15px
  classDef annotation fill:#131a2c,stroke:#4a5580,color:#b0bcd0,font-size:15px
  __multiply_1(("$\times$")):::operator
  __bra_2["$\left\langle \phi\right|$"]
  __multiply_3(("$\times$")):::operator
  A["$\hat{A}$"]:::scalar
  __ket_4["$\left|\psi\right\rangle$"]
  __bra_2 --> __multiply_1
  A --> __multiply_3
  __ket_4 --> __multiply_3
  __multiply_3 --> __multiply_1
  linkStyle 0 stroke:#ef5350,stroke-width:3px
  linkStyle 1 stroke:#ef5350,stroke-width:3px
  linkStyle 2 stroke:#ef5350,stroke-width:3px
  linkStyle 3 stroke:#ef5350,stroke-width:3px

{
  "nodes": [
    {
      "id": "__equals_1",
      "type": "relation",
      "op": "equals",
      "subexpr": "\\hat{A} | a \\rangle = a | a \\rangle",
      "chartScript": {
        "script": "A*hat*|a> - a*|a>",
        "variables": [
          "A",
          "a",
          "hat"
        ]
      }
    },
    {
      "id": "__multiply_2",
      "type": "operator",
      "op": "multiply",
      "subexpr": "\\hat{A} {\\left|a\\right\\rangle }",
      "chartScript": {
        "script": "A*hat*|a>",
        "variables": [
          "A",
          "a",
          "hat"
        ]
      }
    },
    {
      "id": "A",
      "type": "scalar",
      "latex": "\\hat{A}",
      "subexpr": "\\hat{A}",
      "chartScript": {
        "script": "A*hat",
        "variables": [
          "A",
          "hat"
        ]
      }
    },
    {
      "id": "__ket_3",
      "type": "ket",
      "latex": "\\left|a\\right\\rangle",
      "subexpr": "\\left|a\\right\\rangle",
      "chartScript": {
        "script": "|a>",
        "variables": [
          "a"
        ]
      }
    },
    {
      "id": "__multiply_4",
      "type": "operator",
      "op": "multiply",
      "subexpr": "a {\\left|a\\right\\rangle }",
      "chartScript": {
        "script": "a*|a>",
        "variables": [
          "a"
        ]
      }
    },
    {
      "id": "a",
      "type": "scalar",
      "latex": "a",
      "subexpr": "a",
      "chartScript": {
        "script": "a",
        "variables": [
          "a"
        ]
      }
    },
    {
      "id": "__ket_5",
      "type": "ket",
      "latex": "\\left|a\\right\\rangle",
      "subexpr": "\\left|a\\right\\rangle",
      "chartScript": {
        "script": "|a>",
        "variables": [
          "a"
        ]
      }
    }
  ],
  "edges": [
    {
      "from": "A",
      "to": "__multiply_2",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "__ket_3",
      "to": "__multiply_2",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "__multiply_2",
      "to": "__equals_1"
    },
    {
      "from": "a",
      "to": "__multiply_4",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "__ket_5",
      "to": "__multiply_4",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "__multiply_4",
      "to": "__equals_1"
    }
  ],
  "classification": {
    "kind": "algebraic"
  },
  "domain": "quantum_mechanics"
}

flowchart RL
  classDef scalar fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef vector fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef constant fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
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  classDef function fill:#1a2740,stroke:#42a5f5,color:#bbdefb,font-size:15px
  classDef relation fill:#332a0b,stroke:#ffa726,color:#ffe0b2,font-size:15px
  classDef result fill:#332a0b,stroke:#ffa726,color:#ffe0b2,font-size:15px
  classDef annotation fill:#131a2c,stroke:#4a5580,color:#b0bcd0,font-size:15px
  __equals_1{"="}:::relation
  __multiply_2(("$\times$")):::operator
  A["$\hat{A}$"]:::scalar
  __ket_3["$\left|a\right\rangle$"]
  __multiply_4(("$\times$")):::operator
  a["$a$"]:::scalar
  __ket_5["$\left|a\right\rangle$"]
  A --> __multiply_2
  __ket_3 --> __multiply_2
  __multiply_2 --> __equals_1
  a --> __multiply_4
  __ket_5 --> __multiply_4
  __multiply_4 --> __equals_1
  linkStyle 0 stroke:#ef5350,stroke-width:3px
  linkStyle 1 stroke:#ef5350,stroke-width:3px
  linkStyle 2 stroke:#aaa,stroke-width:2px
  linkStyle 3 stroke:#ef5350,stroke-width:3px
  linkStyle 4 stroke:#ef5350,stroke-width:3px
  linkStyle 5 stroke:#aaa,stroke-width:2px

{
  "nodes": [
    {
      "id": "__equals_1",
      "type": "relation",
      "op": "equals",
      "subexpr": "| \\psi \\rangle = \\alpha |0\\rangle + \\beta |1\\rangle",
      "chartScript": {
        "script": "-(alpha*|0> + beta*|1>) + |psi>",
        "variables": [
          "alpha",
          "beta",
          "psi"
        ]
      }
    },
    {
      "id": "__ket_2",
      "type": "ket",
      "latex": "\\left|\\psi\\right\\rangle",
      "subexpr": "\\left|\\psi\\right\\rangle",
      "chartScript": {
        "script": "|psi>",
        "variables": [
          "psi"
        ]
      }
    },
    {
      "id": "__add_3",
      "type": "operator",
      "op": "add",
      "subexpr": "\\alpha {\\left|0\\right\\rangle } + \\beta {\\left|1\\right\\rangle }",
      "chartScript": {
        "script": "alpha*|0> + beta*|1>",
        "variables": [
          "alpha",
          "beta"
        ]
      }
    },
    {
      "id": "__multiply_4",
      "type": "operator",
      "op": "multiply",
      "subexpr": "\\alpha {\\left|0\\right\\rangle }",
      "chartScript": {
        "script": "alpha*|0>",
        "variables": [
          "alpha"
        ]
      }
    },
    {
      "id": "alpha",
      "type": "scalar",
      "latex": "\\alpha",
      "subexpr": "\\alpha",
      "chartScript": {
        "script": "alpha",
        "variables": [
          "alpha"
        ]
      }
    },
    {
      "id": "__ket_5",
      "type": "ket",
      "latex": "\\left|0\\right\\rangle",
      "subexpr": "\\left|0\\right\\rangle",
      "chartScript": {
        "script": "|0>",
        "variables": []
      }
    },
    {
      "id": "__multiply_6",
      "type": "operator",
      "op": "multiply",
      "subexpr": "\\beta {\\left|1\\right\\rangle }",
      "chartScript": {
        "script": "beta*|1>",
        "variables": [
          "beta"
        ]
      }
    },
    {
      "id": "beta",
      "type": "scalar",
      "latex": "\\beta",
      "subexpr": "\\beta",
      "chartScript": {
        "script": "beta",
        "variables": [
          "beta"
        ]
      }
    },
    {
      "id": "__ket_7",
      "type": "ket",
      "latex": "\\left|1\\right\\rangle",
      "subexpr": "\\left|1\\right\\rangle",
      "chartScript": {
        "script": "|1>",
        "variables": []
      }
    }
  ],
  "edges": [
    {
      "from": "__ket_2",
      "to": "__equals_1"
    },
    {
      "from": "alpha",
      "to": "__multiply_4",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "__ket_5",
      "to": "__multiply_4",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "__multiply_4",
      "to": "__add_3"
    },
    {
      "from": "beta",
      "to": "__multiply_6",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "__ket_7",
      "to": "__multiply_6",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "__multiply_6",
      "to": "__add_3"
    },
    {
      "from": "__add_3",
      "to": "__equals_1"
    }
  ],
  "classification": {
    "kind": "algebraic"
  },
  "domain": "quantum_mechanics"
}

flowchart RL
  classDef scalar fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef vector fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef constant fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef number fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef expression fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef text fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
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  classDef function fill:#1a2740,stroke:#42a5f5,color:#bbdefb,font-size:15px
  classDef relation fill:#332a0b,stroke:#ffa726,color:#ffe0b2,font-size:15px
  classDef result fill:#332a0b,stroke:#ffa726,color:#ffe0b2,font-size:15px
  classDef annotation fill:#131a2c,stroke:#4a5580,color:#b0bcd0,font-size:15px
  __equals_1{"="}:::relation
  __ket_2["$\left|\psi\right\rangle$"]
  __add_3(("$+$")):::operator
  __multiply_4(("$\times$")):::operator
  alpha["$\alpha$"]:::scalar
  __ket_5["$\left|0\right\rangle$"]
  __multiply_6(("$\times$")):::operator
  beta["$\beta$"]:::scalar
  __ket_7["$\left|1\right\rangle$"]
  __ket_2 --> __equals_1
  alpha --> __multiply_4
  __ket_5 --> __multiply_4
  __multiply_4 --> __add_3
  beta --> __multiply_6
  __ket_7 --> __multiply_6
  __multiply_6 --> __add_3
  __add_3 --> __equals_1
  linkStyle 0 stroke:#aaa,stroke-width:2px
  linkStyle 1 stroke:#ef5350,stroke-width:3px
  linkStyle 2 stroke:#ef5350,stroke-width:3px
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  linkStyle 4 stroke:#ef5350,stroke-width:3px
  linkStyle 5 stroke:#ef5350,stroke-width:3px
  linkStyle 6 stroke:#aaa,stroke-width:2px
  linkStyle 7 stroke:#aaa,stroke-width:2px

{
  "nodes": [
    {
      "id": "__equals_1",
      "type": "relation",
      "op": "equals",
      "subexpr": "\\hat{H} \\psi = E \\psi",
      "chartScript": {
        "script": "-E*psi + H*hat*psi",
        "variables": [
          "E",
          "H",
          "hat",
          "psi"
        ]
      }
    },
    {
      "id": "__multiply_2",
      "type": "operator",
      "op": "multiply",
      "subexpr": "\\hat{H} \\psi",
      "chartScript": {
        "script": "H*hat*psi",
        "variables": [
          "H",
          "hat",
          "psi"
        ]
      }
    },
    {
      "id": "H",
      "type": "scalar",
      "latex": "\\hat{H}",
      "subexpr": "\\hat{H}",
      "chartScript": {
        "script": "H*hat",
        "variables": [
          "H",
          "hat"
        ]
      }
    },
    {
      "id": "psi",
      "type": "scalar",
      "latex": "\\psi",
      "subexpr": "\\psi",
      "chartScript": {
        "script": "psi",
        "variables": [
          "psi"
        ]
      }
    },
    {
      "id": "__multiply_3",
      "type": "operator",
      "op": "multiply",
      "subexpr": "\\psi E",
      "chartScript": {
        "script": "E*psi",
        "variables": [
          "E",
          "psi"
        ]
      }
    },
    {
      "id": "E",
      "type": "scalar",
      "latex": "E",
      "subexpr": "E",
      "chartScript": {
        "script": "E",
        "variables": [
          "E"
        ]
      }
    }
  ],
  "edges": [
    {
      "from": "H",
      "to": "__multiply_2",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "psi",
      "to": "__multiply_2",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "__multiply_2",
      "to": "__equals_1"
    },
    {
      "from": "E",
      "to": "__multiply_3",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "psi",
      "to": "__multiply_3",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "__multiply_3",
      "to": "__equals_1"
    }
  ],
  "classification": {
    "kind": "algebraic"
  },
  "domain": "quantum_mechanics"
}

flowchart RL
  classDef scalar fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef vector fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef constant fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
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  classDef function fill:#1a2740,stroke:#42a5f5,color:#bbdefb,font-size:15px
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  classDef result fill:#332a0b,stroke:#ffa726,color:#ffe0b2,font-size:15px
  classDef annotation fill:#131a2c,stroke:#4a5580,color:#b0bcd0,font-size:15px
  __equals_1{"="}:::relation
  __multiply_2(("$\times$")):::operator
  H["$\hat{H}$"]:::scalar
  psi["$\psi$"]:::scalar
  __multiply_3(("$\times$")):::operator
  E["$E$"]:::scalar
  H --> __multiply_2
  psi --> __multiply_2
  __multiply_2 --> __equals_1
  E --> __multiply_3
  psi --> __multiply_3
  __multiply_3 --> __equals_1
  linkStyle 0 stroke:#ef5350,stroke-width:3px
  linkStyle 1 stroke:#ef5350,stroke-width:3px
  linkStyle 2 stroke:#aaa,stroke-width:2px
  linkStyle 3 stroke:#ef5350,stroke-width:3px
  linkStyle 4 stroke:#ef5350,stroke-width:3px
  linkStyle 5 stroke:#aaa,stroke-width:2px

{
  "nodes": [
    {
      "id": "__equals_1",
      "type": "relation",
      "op": "equals",
      "subexpr": "\\sigma_x \\sigma_y = i \\sigma_z",
      "chartScript": {
        "script": "-i*sigma_z + sigma_x*sigma_y",
        "variables": [
          "i",
          "sigma_x",
          "sigma_y",
          "sigma_z"
        ]
      }
    },
    {
      "id": "__multiply_2",
      "type": "operator",
      "op": "multiply",
      "subexpr": "\\sigma_{x} \\sigma_{y}",
      "chartScript": {
        "script": "sigma_x*sigma_y",
        "variables": [
          "sigma_x",
          "sigma_y"
        ]
      }
    },
    {
      "id": "sigma_x",
      "type": "scalar",
      "latex": "\\sigma_{x}",
      "subexpr": "\\sigma_{x}",
      "chartScript": {
        "script": "sigma_x",
        "variables": [
          "sigma_x"
        ]
      }
    },
    {
      "id": "sigma_y",
      "type": "scalar",
      "latex": "\\sigma_{y}",
      "subexpr": "\\sigma_{y}",
      "chartScript": {
        "script": "sigma_y",
        "variables": [
          "sigma_y"
        ]
      }
    },
    {
      "id": "__multiply_3",
      "type": "operator",
      "op": "multiply",
      "subexpr": "i \\sigma_{z}",
      "chartScript": {
        "script": "i*sigma_z",
        "variables": [
          "i",
          "sigma_z"
        ]
      }
    },
    {
      "id": "i",
      "type": "scalar",
      "latex": "i",
      "subexpr": "i",
      "chartScript": {
        "script": "i",
        "variables": [
          "i"
        ]
      }
    },
    {
      "id": "sigma_z",
      "type": "scalar",
      "latex": "\\sigma_{z}",
      "subexpr": "\\sigma_{z}",
      "chartScript": {
        "script": "sigma_z",
        "variables": [
          "sigma_z"
        ]
      }
    }
  ],
  "edges": [
    {
      "from": "sigma_x",
      "to": "__multiply_2",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "sigma_y",
      "to": "__multiply_2",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "__multiply_2",
      "to": "__equals_1"
    },
    {
      "from": "i",
      "to": "__multiply_3",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "sigma_z",
      "to": "__multiply_3",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "__multiply_3",
      "to": "__equals_1"
    }
  ],
  "classification": {
    "kind": "algebraic"
  },
  "domain": "quantum_mechanics"
}

flowchart RL
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  classDef vector fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
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  classDef result fill:#332a0b,stroke:#ffa726,color:#ffe0b2,font-size:15px
  classDef annotation fill:#131a2c,stroke:#4a5580,color:#b0bcd0,font-size:15px
  __equals_1{"="}:::relation
  __multiply_2(("$\times$")):::operator
  sigma_x["$\sigma_{x}$"]:::scalar
  sigma_y["$\sigma_{y}$"]:::scalar
  __multiply_3(("$\times$")):::operator
  i["$i$"]:::scalar
  sigma_z["$\sigma_{z}$"]:::scalar
  sigma_x --> __multiply_2
  sigma_y --> __multiply_2
  __multiply_2 --> __equals_1
  i --> __multiply_3
  sigma_z --> __multiply_3
  __multiply_3 --> __equals_1
  linkStyle 0 stroke:#ef5350,stroke-width:3px
  linkStyle 1 stroke:#ef5350,stroke-width:3px
  linkStyle 2 stroke:#aaa,stroke-width:2px
  linkStyle 3 stroke:#ef5350,stroke-width:3px
  linkStyle 4 stroke:#ef5350,stroke-width:3px
  linkStyle 5 stroke:#aaa,stroke-width:2px

{
  "nodes": [
    {
      "id": "__equals_1",
      "type": "relation",
      "op": "equals",
      "subexpr": "\\sigma_x^2 = I",
      "chartScript": {
        "script": "-I + pow(sigma_x, 2)",
        "variables": [
          "I",
          "sigma_x"
        ]
      }
    },
    {
      "id": "__power_2",
      "type": "operator",
      "op": "power",
      "exponent": "2",
      "subexpr": "\\sigma_{x}^{2}",
      "chartScript": {
        "script": "pow(sigma_x, 2)",
        "variables": [
          "sigma_x"
        ]
      }
    },
    {
      "id": "sigma_x",
      "type": "scalar",
      "latex": "\\sigma_{x}",
      "subexpr": "\\sigma_{x}",
      "chartScript": {
        "script": "sigma_x",
        "variables": [
          "sigma_x"
        ]
      }
    },
    {
      "id": "I",
      "type": "scalar",
      "latex": "I",
      "subexpr": "I",
      "chartScript": {
        "script": "I",
        "variables": [
          "I"
        ]
      }
    }
  ],
  "edges": [
    {
      "from": "sigma_x",
      "to": "__power_2"
    },
    {
      "from": "__power_2",
      "to": "__equals_1"
    },
    {
      "from": "I",
      "to": "__equals_1"
    }
  ],
  "classification": {
    "kind": "algebraic"
  },
  "domain": "quantum_mechanics"
}

flowchart RL
  classDef scalar fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef vector fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef constant fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef number fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef expression fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef text fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef operator fill:#1a2740,stroke:#42a5f5,color:#bbdefb,font-size:15px
  classDef function fill:#1a2740,stroke:#42a5f5,color:#bbdefb,font-size:15px
  classDef relation fill:#332a0b,stroke:#ffa726,color:#ffe0b2,font-size:15px
  classDef result fill:#332a0b,stroke:#ffa726,color:#ffe0b2,font-size:15px
  classDef annotation fill:#131a2c,stroke:#4a5580,color:#b0bcd0,font-size:15px
  __equals_1{"="}:::relation
  __power_2(("${(\cdot)}^{2}$")):::operator
  sigma_x["$\sigma_{x}$"]:::scalar
  I["$I$"]:::scalar
  sigma_x --> __power_2
  __power_2 --> __equals_1
  I --> __equals_1
  linkStyle 0 stroke:#aaa,stroke-width:2px
  linkStyle 1 stroke:#ef5350,stroke-width:6px
  linkStyle 2 stroke:#aaa,stroke-width:2px

{
  "nodes": [
    {
      "id": "__equals_1",
      "type": "relation",
      "op": "equals",
      "subexpr": "\\hat{H} = \\frac{\\hat{p}^2}{2m} + V(x)",
      "chartScript": {
        "script": "H*hat - 1/2*hat*pow(p, 2)/m - V(x)",
        "variables": [
          "H",
          "hat",
          "m",
          "p",
          "x"
        ]
      }
    },
    {
      "id": "H",
      "type": "scalar",
      "latex": "\\hat{H}",
      "subexpr": "\\hat{H}",
      "chartScript": {
        "script": "H*hat",
        "variables": [
          "H",
          "hat"
        ]
      }
    },
    {
      "id": "__add_2",
      "type": "operator",
      "op": "add",
      "subexpr": "V{\\left(x \\right)} + \\hat{p}^{2} \\frac{1}{2 m}",
      "chartScript": {
        "script": "V*x + (1/2)*hat*pow(p, 2)/m",
        "variables": [
          "V",
          "hat",
          "m",
          "p",
          "x"
        ]
      }
    },
    {
      "id": "__multiply_3",
      "type": "operator",
      "op": "multiply",
      "subexpr": "\\hat{p}^{2} \\frac{1}{2 m}",
      "chartScript": {
        "script": "(1/2)*hat*pow(p, 2)/m",
        "variables": [
          "hat",
          "m",
          "p"
        ]
      }
    },
    {
      "id": "__power_4",
      "type": "operator",
      "op": "power",
      "exponent": "2",
      "subexpr": "\\hat{p}^{2}",
      "chartScript": {
        "script": "hat*pow(p, 2)",
        "variables": [
          "hat",
          "p"
        ]
      }
    },
    {
      "id": "p",
      "type": "scalar",
      "latex": "\\hat{p}",
      "subexpr": "\\hat{p}",
      "chartScript": {
        "script": "hat*p",
        "variables": [
          "hat",
          "p"
        ]
      }
    },
    {
      "id": "__power_5",
      "type": "operator",
      "latex": "\\dfrac{1}{(\\cdot)}",
      "op": "power",
      "exponent": "-1",
      "subexpr": "\\frac{1}{2 m}",
      "chartScript": {
        "script": "(1/2)/m",
        "variables": [
          "m"
        ]
      }
    },
    {
      "id": "__multiply_6",
      "type": "operator",
      "op": "multiply",
      "subexpr": "m 2",
      "chartScript": {
        "script": "2*m",
        "variables": [
          "m"
        ]
      }
    },
    {
      "id": "__num_7",
      "type": "number",
      "label": "2",
      "subexpr": "2",
      "chartScript": {
        "script": "2",
        "variables": []
      }
    },
    {
      "id": "m",
      "type": "scalar",
      "latex": "m",
      "subexpr": "m",
      "chartScript": {
        "script": "m",
        "variables": [
          "m"
        ]
      }
    },
    {
      "id": "__V_8",
      "type": "function",
      "op": "V",
      "subexpr": "V{\\left(x \\right)}",
      "chartScript": {
        "script": "V*x",
        "variables": [
          "V",
          "x"
        ]
      }
    },
    {
      "id": "x",
      "type": "scalar",
      "latex": "x",
      "subexpr": "x",
      "chartScript": {
        "script": "x",
        "variables": [
          "x"
        ]
      }
    }
  ],
  "edges": [
    {
      "from": "H",
      "to": "__equals_1"
    },
    {
      "from": "p",
      "to": "__power_4"
    },
    {
      "from": "__power_4",
      "to": "__multiply_3",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "__num_7",
      "to": "__multiply_6",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "m",
      "to": "__multiply_6",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "__multiply_6",
      "to": "__power_5"
    },
    {
      "from": "__power_5",
      "to": "__multiply_3"
    },
    {
      "from": "__multiply_3",
      "to": "__add_2"
    },
    {
      "from": "x",
      "to": "__V_8"
    },
    {
      "from": "__V_8",
      "to": "__add_2"
    },
    {
      "from": "__add_2",
      "to": "__equals_1"
    }
  ],
  "classification": {
    "kind": "algebraic"
  },
  "domain": "quantum_mechanics"
}

flowchart RL
  classDef scalar fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef vector fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
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  classDef expression fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
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  classDef function fill:#1a2740,stroke:#42a5f5,color:#bbdefb,font-size:15px
  classDef relation fill:#332a0b,stroke:#ffa726,color:#ffe0b2,font-size:15px
  classDef result fill:#332a0b,stroke:#ffa726,color:#ffe0b2,font-size:15px
  classDef annotation fill:#131a2c,stroke:#4a5580,color:#b0bcd0,font-size:15px
  __equals_1{"="}:::relation
  H["$\hat{H}$"]:::scalar
  __add_2(("$+$")):::operator
  __multiply_3(("$\times$")):::operator
  __power_4(("${(\cdot)}^{2}$")):::operator
  p["$\hat{p}$"]:::scalar
  __power_5(("$\dfrac{1}{(\cdot)}$")):::operator
  __multiply_6(("$\times$")):::operator
  __num_7["$2$"]:::number
  m["$m$"]:::scalar
  __V_8{{"$V(\cdot)$"}}:::function
  x["$x$"]:::scalar
  H --> __equals_1
  p --> __power_4
  __power_4 --> __multiply_3
  __num_7 --> __multiply_6
  m --> __multiply_6
  __multiply_6 --> __power_5
  __power_5 -.-> __multiply_3
  __multiply_3 --> __add_2
  x --> __V_8
  __V_8 --> __add_2
  __add_2 --> __equals_1
  linkStyle 0 stroke:#aaa,stroke-width:2px
  linkStyle 1 stroke:#aaa,stroke-width:2px
  linkStyle 2 stroke:#ef5350,stroke-width:3px
  linkStyle 3 stroke:#ef5350,stroke-width:3px
  linkStyle 4 stroke:#ef5350,stroke-width:3px
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  linkStyle 6 stroke:#42a5f5,stroke-width:1px
  linkStyle 7 stroke:#aaa,stroke-width:2px
  linkStyle 8 stroke:#aaa,stroke-width:2px
  linkStyle 9 stroke:#aaa,stroke-width:2px
  linkStyle 10 stroke:#aaa,stroke-width:2px

{
  "nodes": [
    {
      "id": "__equals_1",
      "type": "relation",
      "op": "equals",
      "subexpr": "E = h \\nu",
      "chartScript": {
        "script": "E - h*nu",
        "variables": [
          "E",
          "h",
          "nu"
        ]
      }
    },
    {
      "id": "E",
      "type": "scalar",
      "latex": "E",
      "subexpr": "E",
      "chartScript": {
        "script": "E",
        "variables": [
          "E"
        ]
      }
    },
    {
      "id": "__multiply_2",
      "type": "operator",
      "op": "multiply",
      "subexpr": "h \\nu",
      "chartScript": {
        "script": "h*nu",
        "variables": [
          "h",
          "nu"
        ]
      }
    },
    {
      "id": "h",
      "type": "scalar",
      "latex": "h",
      "subexpr": "h",
      "chartScript": {
        "script": "h",
        "variables": [
          "h"
        ]
      }
    },
    {
      "id": "nu",
      "type": "scalar",
      "latex": "\\nu",
      "subexpr": "\\nu",
      "chartScript": {
        "script": "nu",
        "variables": [
          "nu"
        ]
      }
    }
  ],
  "edges": [
    {
      "from": "E",
      "to": "__equals_1"
    },
    {
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      "to": "__multiply_2",
      "semantic": "direct",
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    },
    {
      "from": "nu",
      "to": "__multiply_2",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "__multiply_2",
      "to": "__equals_1"
    }
  ],
  "classification": {
    "kind": "algebraic"
  },
  "domain": "quantum_mechanics"
}

flowchart RL
  classDef scalar fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef vector fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef constant fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
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  classDef expression fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
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  classDef function fill:#1a2740,stroke:#42a5f5,color:#bbdefb,font-size:15px
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  classDef result fill:#332a0b,stroke:#ffa726,color:#ffe0b2,font-size:15px
  classDef annotation fill:#131a2c,stroke:#4a5580,color:#b0bcd0,font-size:15px
  __equals_1{"="}:::relation
  E["$E$"]:::scalar
  __multiply_2(("$\times$")):::operator
  h["$h$"]:::scalar
  nu["$\nu$"]:::scalar
  E --> __equals_1
  h --> __multiply_2
  nu --> __multiply_2
  __multiply_2 --> __equals_1
  linkStyle 0 stroke:#aaa,stroke-width:2px
  linkStyle 1 stroke:#ef5350,stroke-width:3px
  linkStyle 2 stroke:#ef5350,stroke-width:3px
  linkStyle 3 stroke:#aaa,stroke-width:2px

{
  "nodes": [
    {
      "id": "__equals_1",
      "type": "relation",
      "op": "equals",
      "subexpr": "\\lambda = \\frac{h}{p}",
      "chartScript": {
        "script": "-h/p + lambda",
        "variables": [
          "h",
          "lambda",
          "p"
        ]
      }
    },
    {
      "id": "lambda",
      "type": "scalar",
      "latex": "\\lambda",
      "subexpr": "\\lambda",
      "chartScript": {
        "script": "lambda",
        "variables": [
          "lambda"
        ]
      }
    },
    {
      "id": "__multiply_2",
      "type": "operator",
      "op": "multiply",
      "subexpr": "h \\frac{1}{p}",
      "chartScript": {
        "script": "h/p",
        "variables": [
          "h",
          "p"
        ]
      }
    },
    {
      "id": "h",
      "type": "scalar",
      "latex": "h",
      "subexpr": "h",
      "chartScript": {
        "script": "h",
        "variables": [
          "h"
        ]
      }
    },
    {
      "id": "__power_3",
      "type": "operator",
      "latex": "\\dfrac{1}{(\\cdot)}",
      "op": "power",
      "exponent": "-1",
      "subexpr": "\\frac{1}{p}",
      "chartScript": {
        "script": "1/p",
        "variables": [
          "p"
        ]
      }
    },
    {
      "id": "p",
      "type": "scalar",
      "latex": "p",
      "subexpr": "p",
      "chartScript": {
        "script": "p",
        "variables": [
          "p"
        ]
      }
    }
  ],
  "edges": [
    {
      "from": "lambda",
      "to": "__equals_1"
    },
    {
      "from": "h",
      "to": "__multiply_2",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "p",
      "to": "__power_3"
    },
    {
      "from": "__power_3",
      "to": "__multiply_2"
    },
    {
      "from": "__multiply_2",
      "to": "__equals_1"
    }
  ],
  "classification": {
    "kind": "algebraic"
  },
  "domain": "quantum_mechanics"
}

flowchart RL
  classDef scalar fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef vector fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef constant fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
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  classDef expression fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
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  __equals_1{"="}:::relation
  lambda["$\lambda$"]:::scalar
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  h["$h$"]:::scalar
  __power_3(("$\dfrac{1}{(\cdot)}$")):::operator
  p["$p$"]:::scalar
  lambda --> __equals_1
  h --> __multiply_2
  p --> __power_3
  __power_3 -.-> __multiply_2
  __multiply_2 --> __equals_1
  linkStyle 0 stroke:#aaa,stroke-width:2px
  linkStyle 1 stroke:#ef5350,stroke-width:3px
  linkStyle 2 stroke:#aaa,stroke-width:2px
  linkStyle 3 stroke:#42a5f5,stroke-width:1px
  linkStyle 4 stroke:#aaa,stroke-width:2px

{
  "nodes": [
    {
      "id": "__equals_1",
      "type": "relation",
      "op": "equals",
      "subexpr": "\\psi(x) = A e^{ikx} + B e^{-ikx}",
      "chartScript": {
        "script": "-A*exp(i*k*x) - B*exp(-i*k*x) + psi(x)",
        "variables": [
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          "B",
          "i",
          "k",
          "x"
        ]
      }
    },
    {
      "id": "__psi_2",
      "type": "function",
      "latex": "\\psi",
      "op": "psi",
      "subexpr": "\\psi{\\left(x \\right)}",
      "chartScript": {
        "script": "psi*x",
        "variables": [
          "psi",
          "x"
        ]
      }
    },
    {
      "id": "x",
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      "latex": "x",
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      "chartScript": {
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        ]
      }
    },
    {
      "id": "__add_3",
      "type": "operator",
      "op": "add",
      "subexpr": "A e^{i k x} + e^{- i k x} B",
      "chartScript": {
        "script": "A*exp(i*k*x) + B*exp(-i*k*x)",
        "variables": [
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          "B",
          "i",
          "k",
          "x"
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      }
    },
    {
      "id": "__multiply_4",
      "type": "operator",
      "op": "multiply",
      "subexpr": "A e^{i k x}",
      "chartScript": {
        "script": "A*exp(i*k*x)",
        "variables": [
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          "i",
          "k",
          "x"
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      }
    },
    {
      "id": "A",
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      "latex": "A",
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      "chartScript": {
        "script": "A",
        "variables": [
          "A"
        ]
      }
    },
    {
      "id": "__power_5",
      "type": "operator",
      "op": "power",
      "subexpr": "e^{i k x}",
      "chartScript": {
        "script": "exp(i*k*x)",
        "variables": [
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          "k",
          "x"
        ]
      }
    },
    {
      "id": "e",
      "type": "scalar",
      "latex": "e",
      "subexpr": "e",
      "chartScript": {
        "script": "e",
        "variables": []
      }
    },
    {
      "id": "__multiply_6",
      "type": "operator",
      "op": "multiply",
      "subexpr": "i x k",
      "chartScript": {
        "script": "i*k*x",
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          "k",
          "x"
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      }
    },
    {
      "id": "i",
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      "latex": "i",
      "subexpr": "i",
      "chartScript": {
        "script": "i",
        "variables": [
          "i"
        ]
      }
    },
    {
      "id": "__multiply_7",
      "type": "operator",
      "op": "multiply",
      "subexpr": "x k",
      "chartScript": {
        "script": "k*x",
        "variables": [
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          "x"
        ]
      }
    },
    {
      "id": "k",
      "type": "scalar",
      "latex": "k",
      "subexpr": "k",
      "chartScript": {
        "script": "k",
        "variables": [
          "k"
        ]
      }
    },
    {
      "id": "__multiply_8",
      "type": "operator",
      "op": "multiply",
      "subexpr": "e^{- i k x} B",
      "chartScript": {
        "script": "B*exp(-i*k*x)",
        "variables": [
          "B",
          "i",
          "k",
          "x"
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      }
    },
    {
      "id": "B",
      "type": "scalar",
      "latex": "B",
      "subexpr": "B",
      "chartScript": {
        "script": "B",
        "variables": [
          "B"
        ]
      }
    },
    {
      "id": "__power_9",
      "type": "operator",
      "op": "power",
      "subexpr": "e^{- i k x}",
      "chartScript": {
        "script": "exp(-i*k*x)",
        "variables": [
          "i",
          "k",
          "x"
        ]
      }
    },
    {
      "id": "__negation_10",
      "type": "operator",
      "op": "negation",
      "subexpr": "-i x k",
      "chartScript": {
        "script": "-i*k*x",
        "variables": [
          "i",
          "k",
          "x"
        ]
      }
    },
    {
      "id": "__multiply_11",
      "type": "operator",
      "op": "multiply",
      "subexpr": "i x k",
      "chartScript": {
        "script": "i*k*x",
        "variables": [
          "i",
          "k",
          "x"
        ]
      }
    }
  ],
  "edges": [
    {
      "from": "x",
      "to": "__psi_2"
    },
    {
      "from": "__psi_2",
      "to": "__equals_1"
    },
    {
      "from": "A",
      "to": "__multiply_4",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "e",
      "to": "__power_5"
    },
    {
      "from": "i",
      "to": "__multiply_6",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "k",
      "to": "__multiply_7",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "x",
      "to": "__multiply_7",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "__multiply_7",
      "to": "__multiply_6",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "__multiply_6",
      "to": "__power_5",
      "role": "exp"
    },
    {
      "from": "__power_5",
      "to": "__multiply_4",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "__multiply_4",
      "to": "__add_3"
    },
    {
      "from": "B",
      "to": "__multiply_8",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "e",
      "to": "__power_9"
    },
    {
      "from": "i",
      "to": "__multiply_11",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "k",
      "to": "__multiply_11",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "x",
      "to": "__multiply_11",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "__multiply_11",
      "to": "__negation_10"
    },
    {
      "from": "__negation_10",
      "to": "__power_9",
      "role": "exp"
    },
    {
      "from": "__power_9",
      "to": "__multiply_8"
    },
    {
      "from": "__multiply_8",
      "to": "__add_3"
    },
    {
      "from": "__add_3",
      "to": "__equals_1"
    }
  ],
  "classification": {
    "kind": "algebraic"
  },
  "domain": "quantum_mechanics"
}

flowchart RL
  classDef scalar fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef vector fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef constant fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef number fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef expression fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
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  classDef function fill:#1a2740,stroke:#42a5f5,color:#bbdefb,font-size:15px
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  classDef annotation fill:#131a2c,stroke:#4a5580,color:#b0bcd0,font-size:15px
  __equals_1{"="}:::relation
  __psi_2{{"$\psi(\cdot)$"}}:::function
  x["$x$"]:::scalar
  __add_3(("$+$")):::operator
  __multiply_4(("$\times$")):::operator
  A["$A$"]:::scalar
  __power_5(("$(\cdot)^{\cdot}$")):::operator
  e["$e$"]:::scalar
  __multiply_6(("$\times$")):::operator
  i["$i$"]:::scalar
  __multiply_7(("$\times$")):::operator
  k["$k$"]:::scalar
  __multiply_8(("$\times$")):::operator
  B["$B$"]:::scalar
  __power_9(("$(\cdot)^{\cdot}$")):::operator
  __negation_10@{ shape: "flip-tri", label: "$-$" }
  __multiply_11(("$\times$")):::operator
  class __negation_10 operator
  x --> __psi_2
  __psi_2 --> __equals_1
  A --> __multiply_4
  e --> __power_5
  i --> __multiply_6
  k --> __multiply_7
  x --> __multiply_7
  __multiply_7 --> __multiply_6
  __multiply_6 -->|exp| __power_5
  __power_5 --> __multiply_4
  __multiply_4 --> __add_3
  B --> __multiply_8
  e --> __power_9
  i --> __multiply_11
  k --> __multiply_11
  x --> __multiply_11
  __multiply_11 --> __negation_10
  __negation_10 -->|exp| __power_9
  __power_9 --> __multiply_8
  __multiply_8 --> __add_3
  __add_3 --> __equals_1
  linkStyle 0 stroke:#aaa,stroke-width:2px
  linkStyle 1 stroke:#aaa,stroke-width:2px
  linkStyle 2 stroke:#ef5350,stroke-width:3px
  linkStyle 3 stroke:#aaa,stroke-width:2px
  linkStyle 4 stroke:#ef5350,stroke-width:3px
  linkStyle 5 stroke:#ef5350,stroke-width:3px
  linkStyle 6 stroke:#ef5350,stroke-width:3px
  linkStyle 7 stroke:#ef5350,stroke-width:3px
  linkStyle 8 stroke:#aaa,stroke-width:2px
  linkStyle 9 stroke:#ef5350,stroke-width:3px
  linkStyle 10 stroke:#aaa,stroke-width:2px
  linkStyle 11 stroke:#ef5350,stroke-width:3px
  linkStyle 12 stroke:#aaa,stroke-width:2px
  linkStyle 13 stroke:#ef5350,stroke-width:3px
  linkStyle 14 stroke:#ef5350,stroke-width:3px
  linkStyle 15 stroke:#ef5350,stroke-width:3px
  linkStyle 16 stroke:#aaa,stroke-width:2px
  linkStyle 17 stroke:#aaa,stroke-width:2px
  linkStyle 18 stroke:#ef5350,stroke-width:3px
  linkStyle 19 stroke:#aaa,stroke-width:2px
  linkStyle 20 stroke:#aaa,stroke-width:2px

{
  "nodes": [
    {
      "id": "__multiply_1",
      "type": "operator",
      "op": "multiply",
      "subexpr": "{\\Delta x} {\\Delta p}",
      "chartScript": {
        "script": "pow(Delta, 2)*p*x",
        "variables": [
          "Delta",
          "p",
          "x"
        ]
      }
    },
    {
      "id": "Delta_x",
      "type": "scalar",
      "latex": "\\Delta x",
      "subexpr": "\\Delta x",
      "chartScript": {
        "script": "Delta*x",
        "variables": [
          "Delta",
          "x"
        ]
      }
    },
    {
      "id": "Delta_p",
      "type": "scalar",
      "latex": "\\Delta p",
      "subexpr": "\\Delta p",
      "chartScript": {
        "script": "Delta*p",
        "variables": [
          "Delta",
          "p"
        ]
      }
    },
    {
      "id": "__multiply_2",
      "type": "operator",
      "op": "multiply",
      "subexpr": "\\frac{\\hbar}{2}",
      "chartScript": {
        "script": "(1/2)*hbar",
        "variables": [
          "hbar"
        ]
      }
    },
    {
      "id": "hbar",
      "type": "scalar",
      "latex": "\\hbar",
      "subexpr": "\\hbar",
      "chartScript": {
        "script": "hbar",
        "variables": [
          "hbar"
        ]
      }
    },
    {
      "id": "__power_3",
      "type": "operator",
      "latex": "\\dfrac{1}{(\\cdot)}",
      "op": "power",
      "exponent": "-1",
      "subexpr": "\\frac{1}{2}",
      "chartScript": {
        "script": "1/2",
        "variables": []
      }
    },
    {
      "id": "__num_4",
      "type": "number",
      "label": "2",
      "subexpr": "2",
      "chartScript": {
        "script": "2",
        "variables": []
      }
    },
    {
      "id": "__greater_equal_5",
      "type": "relation",
      "label": "greater than or equal to",
      "emoji": "≥",
      "op": "greater_equal",
      "subexpr": "\\Delta x \\Delta p \\geq \\frac{\\hbar}{2}",
      "chartScript": {
        "script": "pow(Delta, 2)*p*x - 1/2*hbar",
        "variables": [
          "Delta",
          "hbar",
          "p",
          "x"
        ]
      }
    }
  ],
  "edges": [
    {
      "from": "Delta_x",
      "to": "__multiply_1",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "Delta_p",
      "to": "__multiply_1",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "hbar",
      "to": "__multiply_2",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "__num_4",
      "to": "__power_3"
    },
    {
      "from": "__power_3",
      "to": "__multiply_2"
    },
    {
      "from": "__multiply_1",
      "to": "__greater_equal_5",
      "role": "lhs"
    },
    {
      "from": "__multiply_2",
      "to": "__greater_equal_5",
      "role": "rhs"
    }
  ],
  "classification": {
    "kind": "algebraic"
  },
  "domain": "quantum_mechanics"
}

flowchart RL
  classDef scalar fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef vector fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef constant fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef number fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef expression fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef text fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef operator fill:#1a2740,stroke:#42a5f5,color:#bbdefb,font-size:15px
  classDef function fill:#1a2740,stroke:#42a5f5,color:#bbdefb,font-size:15px
  classDef relation fill:#332a0b,stroke:#ffa726,color:#ffe0b2,font-size:15px
  classDef result fill:#332a0b,stroke:#ffa726,color:#ffe0b2,font-size:15px
  classDef annotation fill:#131a2c,stroke:#4a5580,color:#b0bcd0,font-size:15px
  __multiply_1(("$\times$")):::operator
  Delta_x["$\Delta x$"]:::scalar
  Delta_p["$\Delta p$"]:::scalar
  __multiply_2(("$\times$")):::operator
  hbar["$\hbar$"]:::scalar
  __power_3(("$\dfrac{1}{(\cdot)}$")):::operator
  __num_4["$2$"]:::number
  __greater_equal_5{"≥"}:::relation
  Delta_x --> __multiply_1
  Delta_p --> __multiply_1
  hbar --> __multiply_2
  __num_4 --> __power_3
  __power_3 -.-> __multiply_2
  __multiply_1 -->|lhs| __greater_equal_5
  __multiply_2 -->|rhs| __greater_equal_5
  linkStyle 0 stroke:#ef5350,stroke-width:3px
  linkStyle 1 stroke:#ef5350,stroke-width:3px
  linkStyle 2 stroke:#ef5350,stroke-width:3px
  linkStyle 3 stroke:#aaa,stroke-width:2px
  linkStyle 4 stroke:#42a5f5,stroke-width:1px
  linkStyle 5 stroke:#aaa,stroke-width:2px
  linkStyle 6 stroke:#aaa,stroke-width:2px

{
  "nodes": [
    {
      "id": "__equals_1",
      "type": "relation",
      "op": "equals",
      "subexpr": "E = \\frac{hc}{\\lambda}",
      "chartScript": {
        "script": "E - c*h/lambda",
        "variables": [
          "E",
          "c",
          "h",
          "lambda"
        ]
      }
    },
    {
      "id": "E",
      "type": "scalar",
      "latex": "E",
      "subexpr": "E",
      "chartScript": {
        "script": "E",
        "variables": [
          "E"
        ]
      }
    },
    {
      "id": "__multiply_2",
      "type": "operator",
      "op": "multiply",
      "subexpr": "\\frac{1}{\\lambda} c h",
      "chartScript": {
        "script": "c*h/lambda",
        "variables": [
          "c",
          "h",
          "lambda"
        ]
      }
    },
    {
      "id": "__multiply_3",
      "type": "operator",
      "op": "multiply",
      "subexpr": "c h",
      "chartScript": {
        "script": "c*h",
        "variables": [
          "c",
          "h"
        ]
      }
    },
    {
      "id": "h",
      "type": "scalar",
      "latex": "h",
      "subexpr": "h",
      "chartScript": {
        "script": "h",
        "variables": [
          "h"
        ]
      }
    },
    {
      "id": "c",
      "type": "scalar",
      "latex": "c",
      "subexpr": "c",
      "chartScript": {
        "script": "c",
        "variables": [
          "c"
        ]
      }
    },
    {
      "id": "__power_4",
      "type": "operator",
      "latex": "\\dfrac{1}{(\\cdot)}",
      "op": "power",
      "exponent": "-1",
      "subexpr": "\\frac{1}{\\lambda}",
      "chartScript": {
        "script": "1/lambda",
        "variables": [
          "lambda"
        ]
      }
    },
    {
      "id": "lambda",
      "type": "scalar",
      "latex": "\\lambda",
      "subexpr": "\\lambda",
      "chartScript": {
        "script": "lambda",
        "variables": [
          "lambda"
        ]
      }
    }
  ],
  "edges": [
    {
      "from": "E",
      "to": "__equals_1"
    },
    {
      "from": "h",
      "to": "__multiply_3",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "c",
      "to": "__multiply_3",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "__multiply_3",
      "to": "__multiply_2",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "lambda",
      "to": "__power_4"
    },
    {
      "from": "__power_4",
      "to": "__multiply_2"
    },
    {
      "from": "__multiply_2",
      "to": "__equals_1"
    }
  ],
  "classification": {
    "kind": "algebraic"
  },
  "domain": "quantum_mechanics"
}

flowchart RL
  classDef scalar fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef vector fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef constant fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef number fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef expression fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef text fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
  classDef operator fill:#1a2740,stroke:#42a5f5,color:#bbdefb,font-size:15px
  classDef function fill:#1a2740,stroke:#42a5f5,color:#bbdefb,font-size:15px
  classDef relation fill:#332a0b,stroke:#ffa726,color:#ffe0b2,font-size:15px
  classDef result fill:#332a0b,stroke:#ffa726,color:#ffe0b2,font-size:15px
  classDef annotation fill:#131a2c,stroke:#4a5580,color:#b0bcd0,font-size:15px
  __equals_1{"="}:::relation
  E["$E$"]:::scalar
  __multiply_2(("$\times$")):::operator
  __multiply_3(("$\times$")):::operator
  h["$h$"]:::scalar
  c["$c$"]:::scalar
  __power_4(("$\dfrac{1}{(\cdot)}$")):::operator
  lambda["$\lambda$"]:::scalar
  E --> __equals_1
  h --> __multiply_3
  c --> __multiply_3
  __multiply_3 --> __multiply_2
  lambda --> __power_4
  __power_4 -.-> __multiply_2
  __multiply_2 --> __equals_1
  linkStyle 0 stroke:#aaa,stroke-width:2px
  linkStyle 1 stroke:#ef5350,stroke-width:3px
  linkStyle 2 stroke:#ef5350,stroke-width:3px
  linkStyle 3 stroke:#ef5350,stroke-width:3px
  linkStyle 4 stroke:#aaa,stroke-width:2px
  linkStyle 5 stroke:#42a5f5,stroke-width:1px
  linkStyle 6 stroke:#aaa,stroke-width:2px

{
  "nodes": [
    {
      "id": "__equals_1",
      "type": "relation",
      "op": "equals",
      "subexpr": "E_n = \\frac{n^2 h^2}{8 m L^2}",
      "chartScript": {
        "script": "E_n - 1/8*pow(h, 2)*pow(n, 2)/(pow(L, 2)*m)",
        "variables": [
          "E_n",
          "L",
          "h",
          "m",
          "n"
        ]
      }
    },
    {
      "id": "E_n",
      "type": "scalar",
      "latex": "E_{n}",
      "subexpr": "E_{n}",
      "chartScript": {
        "script": "E_n",
        "variables": [
          "E_n"
        ]
      }
    },
    {
      "id": "__multiply_2",
      "type": "operator",
      "op": "multiply",
      "subexpr": "n^{2} h^{2} \\frac{1}{8 L^{2} m}",
      "chartScript": {
        "script": "(1/8)*pow(h, 2)*pow(n, 2)/(pow(L, 2)*m)",
        "variables": [
          "L",
          "h",
          "m",
          "n"
        ]
      }
    },
    {
      "id": "__multiply_3",
      "type": "operator",
      "op": "multiply",
      "subexpr": "n^{2} h^{2}",
      "chartScript": {
        "script": "pow(h, 2)*pow(n, 2)",
        "variables": [
          "h",
          "n"
        ]
      }
    },
    {
      "id": "__power_4",
      "type": "operator",
      "op": "power",
      "exponent": "2",
      "subexpr": "n^{2}",
      "chartScript": {
        "script": "pow(n, 2)",
        "variables": [
          "n"
        ]
      }
    },
    {
      "id": "n",
      "type": "scalar",
      "latex": "n",
      "subexpr": "n",
      "chartScript": {
        "script": "n",
        "variables": [
          "n"
        ]
      }
    },
    {
      "id": "__power_5",
      "type": "operator",
      "op": "power",
      "exponent": "2",
      "subexpr": "h^{2}",
      "chartScript": {
        "script": "pow(h, 2)",
        "variables": [
          "h"
        ]
      }
    },
    {
      "id": "h",
      "type": "scalar",
      "latex": "h",
      "subexpr": "h",
      "chartScript": {
        "script": "h",
        "variables": [
          "h"
        ]
      }
    },
    {
      "id": "__power_6",
      "type": "operator",
      "latex": "\\dfrac{1}{(\\cdot)}",
      "op": "power",
      "exponent": "-1",
      "subexpr": "\\frac{1}{8 L^{2} m}",
      "chartScript": {
        "script": "(1/8)/(pow(L, 2)*m)",
        "variables": [
          "L",
          "m"
        ]
      }
    },
    {
      "id": "__multiply_7",
      "type": "operator",
      "op": "multiply",
      "subexpr": "8 m L^{2}",
      "chartScript": {
        "script": "8*pow(L, 2)*m",
        "variables": [
          "L",
          "m"
        ]
      }
    },
    {
      "id": "__num_8",
      "type": "number",
      "label": "8",
      "subexpr": "8",
      "chartScript": {
        "script": "8",
        "variables": []
      }
    },
    {
      "id": "__multiply_9",
      "type": "operator",
      "op": "multiply",
      "subexpr": "m L^{2}",
      "chartScript": {
        "script": "pow(L, 2)*m",
        "variables": [
          "L",
          "m"
        ]
      }
    },
    {
      "id": "m",
      "type": "scalar",
      "latex": "m",
      "subexpr": "m",
      "chartScript": {
        "script": "m",
        "variables": [
          "m"
        ]
      }
    },
    {
      "id": "__power_10",
      "type": "operator",
      "op": "power",
      "exponent": "2",
      "subexpr": "L^{2}",
      "chartScript": {
        "script": "pow(L, 2)",
        "variables": [
          "L"
        ]
      }
    },
    {
      "id": "L",
      "type": "scalar",
      "latex": "L",
      "subexpr": "L",
      "chartScript": {
        "script": "L",
        "variables": [
          "L"
        ]
      }
    }
  ],
  "edges": [
    {
      "from": "E_n",
      "to": "__equals_1"
    },
    {
      "from": "n",
      "to": "__power_4"
    },
    {
      "from": "__power_4",
      "to": "__multiply_3",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "h",
      "to": "__power_5"
    },
    {
      "from": "__power_5",
      "to": "__multiply_3",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "__multiply_3",
      "to": "__multiply_2",
      "semantic": "direct",
      "weight": 1.0
    },
    {
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      "to": "__multiply_7",
      "semantic": "direct",
      "weight": 1.0
    },
    {
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      "to": "__multiply_9",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "L",
      "to": "__power_10"
    },
    {
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      "to": "__multiply_9",
      "semantic": "direct",
      "weight": 1.0
    },
    {
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      "to": "__multiply_7",
      "semantic": "direct",
      "weight": 1.0
    },
    {
      "from": "__multiply_7",
      "to": "__power_6"
    },
    {
      "from": "__power_6",
      "to": "__multiply_2"
    },
    {
      "from": "__multiply_2",
      "to": "__equals_1"
    }
  ],
  "classification": {
    "kind": "algebraic"
  },
  "domain": "quantum_mechanics"
}

flowchart RL
  classDef scalar fill:#1b3a1e,stroke:#66bb6a,color:#c8e6c9,font-size:15px
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  __equals_1{"="}:::relation
  E_n["$E_{n}$"]:::scalar
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  __multiply_3(("$\times$")):::operator
  __power_4(("${(\cdot)}^{2}$")):::operator
  n["$n$"]:::scalar
  __power_5(("${(\cdot)}^{2}$")):::operator
  h["$h$"]:::scalar
  __power_6(("$\dfrac{1}{(\cdot)}$")):::operator
  __multiply_7(("$\times$")):::operator
  __num_8["$8$"]:::number
  __multiply_9(("$\times$")):::operator
  m["$m$"]:::scalar
  __power_10(("${(\cdot)}^{2}$")):::operator
  L["$L$"]:::scalar
  E_n --> __equals_1
  n --> __power_4
  __power_4 --> __multiply_3
  h --> __power_5
  __power_5 --> __multiply_3
  __multiply_3 --> __multiply_2
  __num_8 --> __multiply_7
  m --> __multiply_9
  L --> __power_10
  __power_10 --> __multiply_9
  __multiply_9 --> __multiply_7
  __multiply_7 --> __power_6
  __power_6 -.-> __multiply_2
  __multiply_2 --> __equals_1
  linkStyle 0 stroke:#aaa,stroke-width:2px
  linkStyle 1 stroke:#aaa,stroke-width:2px
  linkStyle 2 stroke:#ef5350,stroke-width:3px
  linkStyle 3 stroke:#aaa,stroke-width:2px
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  linkStyle 11 stroke:#aaa,stroke-width:2px
  linkStyle 12 stroke:#42a5f5,stroke-width:1px
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{
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    {
      "id": "__equals_1",
      "type": "relation",
      "op": "equals",
      "subexpr": "\\hbar = \\frac{h}{2\\pi}",
      "chartScript": {
        "script": "-1/2*h/pi + hbar",
        "variables": [
          "h",
          "hbar"
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      }
    },
    {
      "id": "hbar",
      "type": "scalar",
      "latex": "\\hbar",
      "subexpr": "\\hbar",
      "chartScript": {
        "script": "hbar",
        "variables": [
          "hbar"
        ]
      }
    },
    {
      "id": "__multiply_2",
      "type": "operator",
      "op": "multiply",
      "subexpr": "h \\frac{1}{2 \\pi}",
      "chartScript": {
        "script": "(1/2)*h/pi",
        "variables": [
          "h"
        ]
      }
    },
    {
      "id": "h",
      "type": "scalar",
      "latex": "h",
      "subexpr": "h",
      "chartScript": {
        "script": "h",
        "variables": [
          "h"
        ]
      }
    },
    {
      "id": "__power_3",
      "type": "operator",
      "latex": "\\dfrac{1}{(\\cdot)}",
      "op": "power",
      "exponent": "-1",
      "subexpr": "\\frac{1}{2 \\pi}",
      "chartScript": {
        "script": "(1/2)/pi",
        "variables": []
      }
    },
    {
      "id": "__multiply_4",
      "type": "operator",
      "op": "multiply",
      "subexpr": "\\pi 2",
      "chartScript": {
        "script": "2*pi",
        "variables": []
      }
    },
    {
      "id": "__num_5",
      "type": "number",
      "label": "2",
      "subexpr": "2",
      "chartScript": {
        "script": "2",
        "variables": []
      }
    },
    {
      "id": "pi",
      "type": "constant",
      "latex": "\\pi",
      "subexpr": "\\pi",
      "chartScript": {
        "script": "pi",
        "variables": []
      }
    }
  ],
  "edges": [
    {
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    {
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    },
    {
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    },
    {
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      "to": "__equals_1"
    }
  ],
  "classification": {
    "kind": "algebraic"
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  "domain": "quantum_mechanics"
}

flowchart RL
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  __equals_1{"="}:::relation
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  h["$h$"]:::scalar
  __power_3(("$\dfrac{1}{(\cdot)}$")):::operator
  __multiply_4(("$\times$")):::operator
  __num_5["$2$"]:::number
  pi["$\pi$"]:::constant
  hbar --> __equals_1
  h --> __multiply_2
  __num_5 --> __multiply_4
  pi --> __multiply_4
  __multiply_4 --> __power_3
  __power_3 -.-> __multiply_2
  __multiply_2 --> __equals_1
  linkStyle 0 stroke:#aaa,stroke-width:2px
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{
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    {
      "id": "__equals_1",
      "type": "relation",
      "op": "equals",
      "subexpr": "E = \\frac{p^2}{2m}",
      "chartScript": {
        "script": "E - 1/2*pow(p, 2)/m",
        "variables": [
          "E",
          "m",
          "p"
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      }
    },
    {
      "id": "E",
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      "latex": "E",
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      "chartScript": {
        "script": "E",
        "variables": [
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      }
    },
    {
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      "subexpr": "p^{2} \\frac{1}{2 m}",
      "chartScript": {
        "script": "(1/2)*pow(p, 2)/m",
        "variables": [
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          "p"
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      }
    },
    {
      "id": "__power_3",
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      "subexpr": "p^{2}",
      "chartScript": {
        "script": "pow(p, 2)",
        "variables": [
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      }
    },
    {
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    },
    {
      "id": "__power_4",
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      "chartScript": {
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      }
    },
    {
      "id": "__multiply_5",
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      "op": "multiply",
      "subexpr": "m 2",
      "chartScript": {
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        "variables": [
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    },
    {
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      "type": "number",
      "label": "2",
      "subexpr": "2",
      "chartScript": {
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        "variables": []
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    },
    {
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      "type": "scalar",
      "latex": "m",
      "subexpr": "m",
      "chartScript": {
        "script": "m",
        "variables": [
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  "edges": [
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    {
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    },
    {
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    {
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    }
  ],
  "classification": {
    "kind": "algebraic"
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  "domain": "quantum_mechanics"
}

flowchart RL
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  __equals_1{"="}:::relation
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  p["$p$"]:::scalar
  __power_4(("$\dfrac{1}{(\cdot)}$")):::operator
  __multiply_5(("$\times$")):::operator
  __num_6["$2$"]:::number
  m["$m$"]:::scalar
  E --> __equals_1
  p --> __power_3
  __power_3 --> __multiply_2
  __num_6 --> __multiply_5
  m --> __multiply_5
  __multiply_5 --> __power_4
  __power_4 -.-> __multiply_2
  __multiply_2 --> __equals_1
  linkStyle 0 stroke:#aaa,stroke-width:2px
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{
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    {
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      "type": "relation",
      "op": "equals",
      "subexpr": "\\sum_{n=0}^{\\infty} | n \\rangle \\langle n | = I",
      "chartScript": {
        "script": "-I + Sum(|n><n|, (n, 0, Number.POSITIVE_INFINITY))",
        "variables": [
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      }
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    {
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        ]
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    },
    {
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      }
    },
    {
      "id": "__const_4",
      "type": "constant",
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      "chartScript": {
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        "variables": []
      }
    },
    {
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      "type": "relation",
      "op": "equals",
      "subexpr": "n = 0",
      "chartScript": {
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        "variables": [
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    },
    {
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      "type": "operator",
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      "with_respect_to": "n",
      "lower_bound": "__num_3",
      "upper_bound": "__const_4",
      "subexpr": "\\sum_{n=0}^{\\infty} {\\left|n\\right\\rangle }{\\left\\langle n\\right|}",
      "chartScript": {
        "script": "Sum(|n><n|, (n, 0, Number.POSITIVE_INFINITY))",
        "variables": []
      }
    },
    {
      "id": "__outer_product_6",
      "type": "operator",
      "latex": "\\otimes",
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      "chartScript": {
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        "variables": [
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      }
    },
    {
      "id": "__ket_7",
      "type": "ket",
      "latex": "\\left|n\\right\\rangle",
      "subexpr": "\\left|n\\right\\rangle",
      "chartScript": {
        "script": "|n>",
        "variables": [
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    },
    {
      "id": "__bra_8",
      "type": "bra",
      "latex": "\\left\\langle n\\right|",
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      "chartScript": {
        "script": "<n|",
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        ]
      }
    },
    {
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      "chartScript": {
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        "variables": [
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    {
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    {
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    {
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    "kind": "algebraic"
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}

flowchart RL
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  __equals_5{"="}:::relation
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  __outer_product_6(("$\otimes$")):::operator
  __ket_7["$\left|n\right\rangle$"]
  __bra_8["$\left\langle n\right|$"]
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  n -->|wrt| __sum_2
  n --> __equals_5
  __num_3 --> __equals_5
  __equals_5 -->|lb| __sum_2
  __const_4 -->|ub| __sum_2
  __ket_7 -->|lhs| __outer_product_6
  __bra_8 -->|rhs| __outer_product_6
  __outer_product_6 --> __sum_2
  __sum_2 --> __equals_1
  I --> __equals_1
  linkStyle 0 stroke:#aaa,stroke-width:2px
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