# Author: Alex Gezerlis

# Numerical Methods in Physics with Python (CUP, 2020)

from math import sqrt, pi, factorial, exp

import cmath

def hermite(n,x):

val0 = 1.; val1 = 2*x

for j in range(1,n):

val2 = 2*x*val1 - 2*j*val0

val0, val1 = val1, val2

dval2 = 2*n*val0

return val2, dval2

def psiqho(x,nametoval):

n = nametoval["n"]

momohbar = nametoval["momohbar"]

al = nametoval["al"]

psival = momohbar**0.25*exp(-0.5*al*momohbar * x**2)

psival *= hermite(n,sqrt(momohbar)*x)[0]

psival /= sqrt(2**n * factorial(n) * sqrt(pi))

return psival

def psibox(x,nametoval):

n = nametoval["n"]

boxl = nametoval["boxl"]

return cmath.exp(2*pi*n*x*1j/boxl)

if __name__ == '__main__':

x = 1.

nametoval = {"n": 100, "momohbar": 1., "al": 1.}

psiA = psiqho(x, nametoval)

nametoval = {"n": -2, "boxl": 2*pi}

psiB = psibox(x, nametoval)

print(psiA, psiB)