Quantum Harmonic Oscillator Animation

gistfile1.txt

// use typescript
// use math.js

import math from "mathjs";


//         a
//    a1      a2            b          c             d
// (2^n*n!)^(-1/2) * Pi^(-1/4) * Exp[-x^2/2] * HermiteH[n, x];
function psi(n: number, x: number) {
  const nf = math.factorial(n) as number;
  const a1 = Math.pow(2, n * nf);
  const a2 = -1 / 2;
  const a = Math.pow(a1, a2);

  const b = Math.pow(Math.PI, -1 / 4);
  const c = Math.exp(Math.pow(-x, 2) / 2);
  const d = computeHermite(n, x);

  return a * b * c * d;
}

function energy(n: number) {
  return n + 1 / 2;
}

// psit: psi[n, x] Exp[-I*energy[n]*t]
function psit(n: number, x: number, t: number) {
  const n1 = psi(n, x);
  const i = math.multiply(-1, math.sqrt(-1));
  const e = energy(n);
  const n2 = math.exp(math.multiply(math.multiply(i, e), t));

  const ret = math.multiply(n1, n2);
  return ret;
}

// Im[psit[1, x, t]]
export function graphD(x: number, t: number, amplitude: number) {
  const _x = fit(x, 0, 1, -5, 5);
  const y = (math.multiply(psit(1, _x, t), 1) as any).im;
  return y;
}


console.log("x:0,  t: 0,   f(x, t): ", graphD(0, 0, 10));
console.log("x:-2, t: 0,   f(x, t): ", graphD(-2, 0, 10));
console.log("x:2,  t: 0,   f(x, t): ", graphD(2, 0, 10));

console.log("x:0,  t: 0.5, f(x, t): ", graphD(0, 0.5, 10));
console.log("x:-2, t: 0.5, f(x, t): ", graphD(-2, 0.5, 10));
console.log("x:2,  t: 0.5, f(x, t): ", graphD(2, 0.5, 10));

console.log("x:0,  t: 1,   f(x, t): ", graphD(0, 1, 10));
console.log("x:-2, t: 1,   f(x, t): ", graphD(-2, 1, 10));
console.log("x:2,  t: 1,   f(x, t): ", graphD(2, 1, 10));