一维无限深势井中的电子python

以下是一维无限深势井中的电子的Python代码示例：

import numpy as np
import matplotlib.pyplot as plt

# Define constants
hbar = 1.055e-34  # Planck's constant divided by 2*pi
m = 9.11e-31  # electron mass
L = 1e-8  # well width
N = 1000  # number of grid points
x = np.linspace(0, L, N)  # grid points
dx = x[1] - x[0]  # grid spacing

# Define potential
V = np.zeros(N)  # infinite potential well

# Define wavefunction
psi = np.zeros(N)
psi[0] = 1.0  # wavefunction at left boundary
psi[N-1] = 0.0  # wavefunction at right boundary

# Define time evolution parameters
t = 0.0
dt = 1e-19  # time step
T = 1e-17  # total time

# Define plot window
plt.ion()
fig, ax = plt.subplots()
line, = ax.plot(x, psi)

# Time evolution loop
while t < T:
    # Calculate second derivative of wavefunction
    d2psi = (psi[0:N-2] - 2*psi[1:N-1] + psi[2:N]) / dx**2

    # Update wavefunction using time-dependent Schrodinger equation
    psi[1:N-1] += -1j/hbar * dt * (d2psi + V[1:N-1]*psi[1:N-1])

    # Normalize wavefunction
    psi /= np.sqrt(np.sum(np.abs(psi)**2)*dx)

    # Update time and plot wavefunction
    t += dt
    line.set_ydata(psi)
    fig.canvas.draw()
    fig.canvas.flush_events()

# Plot final wavefunction
plt.ioff()
plt.figure()
plt.plot(x, np.abs(psi)**2)
plt.xlabel('Position')
plt.ylabel('Probability density')
plt.show()

该代码使用有限差分方法对一维无限深势井中的电子进行模拟。它通过离散化空间和时间来计算波函数的演化，并使用matplotlib库将波函数实时绘制出来。最后，它绘制了波函数的概率密度分布。