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{
  "type": "doc",
  "content": [
    {
      "type": "heading",
      "attrs": {
        "level": 2
      },
      "content": [
        {
          "type": "text",
          "text": "A worked example"
        }
      ]
    },
    {
      "type": "paragraph",
      "content": [
        {
          "type": "text",
          "text": "The Gaussian integral is "
        },
        {
          "type": "mathInline",
          "attrs": {
            "tex": "\\int_{-\\infty}^{\\infty} e^{-x^2}\\,dx = \\sqrt{\\pi}"
          }
        },
        {
          "type": "text",
          "text": ", a staple of probability."
        }
      ]
    },
    {
      "type": "mathBlock",
      "attrs": {
        "tex": "i\\hbar\\frac{\\partial}{\\partial t}\\Psi = \\hat{H}\\Psi"
      }
    },
    {
      "type": "theoremBlock",
      "attrs": {
        "kind": "theorem",
        "title": "Cauchy–Schwarz"
      },
      "content": [
        {
          "type": "paragraph",
          "content": [
            {
              "type": "text",
              "text": "For all vectors "
            },
            {
              "type": "mathInline",
              "attrs": {
                "tex": "\\mathbf{u},\\mathbf{v}"
              }
            },
            {
              "type": "text",
              "text": " in an inner product space:"
            }
          ]
        },
        {
          "type": "mathBlock",
          "attrs": {
            "tex": "|\\langle \\mathbf{u},\\mathbf{v}\\rangle|^2 \\leq \\langle \\mathbf{u},\\mathbf{u}\\rangle\\,\\langle \\mathbf{v},\\mathbf{v}\\rangle"
          }
        }
      ]
    }
  ]
}