simulate: Electron double slit experiment

Here’s an example Python program that simulates the double-slit experiment for electrons using the Monte Carlo method:

pythonCopy codeimport numpy as np
import matplotlib.pyplot as plt

# Define the constants and parameters
hbar = 1.054e-34  # Planck's constant over 2*pi
me = 9.11e-31     # Mass of electron
L = 1e-8          # Distance from slit to screen
d = 1e-9          # Distance between slits
lambda_ = 5e-10   # Wavelength of electron

# Define the probability amplitude function
def psi(x):
    return np.exp(2*np.pi*1j*x/lambda_)/np.sqrt(2*np.pi)

# Define the simulation parameters
N = 10000         # Number of electrons
a = 2*d           # Width of the slits
sigma = 0.1*a     # Standard deviation of the electron beam

# Generate the initial positions and velocities of the electrons
x0 = np.random.normal(0, sigma, size=N)
y0 = np.zeros_like(x0)
vx0 = np.zeros_like(x0)
vy0 = np.sqrt(2*me*10)/me  # Assume a vertical velocity of 10 m/s

# Simulate the electron trajectories
x = np.zeros((N, 2))
v = np.zeros_like(x)
x[:, 0] = x0
v[:, 0] = vx0
for i in range(1, 100):
    x[:, i] = x[:, i-1] + v[:, i-1]*1e-12
    v[:, i] = v[:, i-1]

# Calculate the probability density on the screen
y = np.linspace(-L/2, L/2, 1000)
P = np.zeros_like(y)
for i in range(N):
    for j in range(len(y)):
        r1 = np.sqrt((x[i,-1] - d)**2 + (y[j] - y0[i])**2)
        r2 = np.sqrt((x[i,-1] + d)**2 + (y[j] - y0[i])**2)
        P[j] += abs(psi(r1) + psi(r2))**2

# Plot the results
plt.plot(y, P)
plt.xlabel('Position on screen (m)')
plt.ylabel('Probability density')
plt.show()

This program generates N electrons with a Gaussian distribution of initial positions and velocities, and simulates their trajectories using a simple Euler method. The probability density on the screen is then calculated by summing the squared magnitudes of the probability amplitudes for each electron at each point on the screen.

Note that this is a simplified model that assumes a single frequency and energy for the electrons, and ignores factors such as electron-electron interactions and the effects of the screen on the electron trajectories. However, it should provide a basic demonstration of the principles of the double-slit experiment.