a derivation and computation of the wave function's vertices over different time steps, plotting them in three dimensions.

import numpy as np
import matplotlib.pyplot as plt

# Set the background color using rc parameters
plt.style.use('dark_background')
plt.rcParams['axes.facecolor'] = '#191919'
plt.rcParams['figure.facecolor'] = '#191919'

# Constants
sigma = 2
c = 1
hbar = 1
m = 1
p = 4

def wavefunction(x, t, p):
i = complex(0., 1.)
factor = np.sqrt(np.pi / (1. / (2. * sigma**2)) + i * t / (hbar * m))
exponential = np.exp(-x**2 * sigma**2 / (2. * hbar * (1. + i * t * sigma**2) / (hbar * m))
+ i * p * x / (sigma**2 * hbar * (1. + i * t * sigma**2) / (hbar * m)))

return c * factor * exponential

# Variables
x_values = np.arange(-50. * sigma, 50. * sigma, 0.01 * sigma)
deltat = .1
tf = deltat * 50

plt.ion()
with open('gaussianpsi.txt', 'w') as f:
while True: # Infinite loop for continuous animation
t = 0
while t < tf:
plt.pause(.0001)
plt.cla()
y_values = wavefunction(x_values, t, p)

plt.plot(x_values, y_values.real, label='Real Part', color='#fff', linestyle='-')
plt.plot(x_values, y_values.imag, label='Imaginary Part', color='#fff', linestyle='--')
plt.ylim(ymin=-10., ymax=10.)
plt.legend() # Show legend indicating the colors

for x_val, y_val in zip(x_values, y_values):
s = '{: E},{: E},{: E},{: E}
'.format(t, x_val, y_val.real, y_val.imag)
f.write(s)

t += deltat