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@dougmcnally /QHO.py
Last active May 17, 2016

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Source code to generate plots of the Quantum Harmonic Oscillator wavefunction. Here's a brief description of what that is: http://ket.space/index.php/2016/05/17/quantum-harmonic-oscillator/
from __future__ import division
from numpy.polynomial.hermite import *
import numpy
import pylab
import math
# use natural units where c = h_bar = 1
m = 1
w = 1
h_bar = 1
n = 1
# some realistic values in SI units might be:
# mass of the electron m = 9.11e-31 kg
# Planck's constant h_bar = 1.05e-34 J s
# natural frequency of the oscillator w = 4.57e14 Hz
# more info on QHO here: https://en.wikipedia.org/wiki/Quantum_harmonic_oscillator
pi = math.pi
x_min = -20
x_max = -x_min
xs = numpy.linspace(x_min,x_max,10000)
psi = []
# coefficients for Hermite series, all 0s except the n-th term
herm_coeff = []
for i in range(n):
herm_coeff.append(0)
herm_coeff.append(1)
for x in xs:
psi.append(math.exp(-m*w*x**2/(2*h_bar)) * hermval((m*w/h_bar)**0.5 * x, herm_coeff))
# normalization factor for the wavefunction:
psi = numpy.multiply(psi, 1 / (math.pow(2, n) * math.factorial(n))**0.5 * (m*w/(pi*h_bar))**0.25)
pylab.plot(xs, psi)
pylab.xlim(xmax=x_max, xmin=x_min)
pylab.xlabel("$x$", size=18)
pylab.ylabel("$\psi_{" + str(n) + "}(x)$", size=18)
pylab.title("Quantum Harmonic Oscillator Wavefunction ($n = " + str(n) + "$)", size=14)
pylab.savefig("QHOn=" + str(n) + ".png",bbox_inches="tight",dpi=600)
pylab.show()
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