quantum-dev/ps9-2.py

import numpy as np

a = 1
hbar = 1  # 1.054572e-34
n_vals = [n for n in range(1, 7)]

N = 1000
dx = 1 / N
x_vals = np.linspace(-a / 2, a / 2, N)

psi_funcs = []
psi_derivs = []
psi_2nd_derivs = []
for n in n_vals:
    if n % 2 == 0:
        psi_funcs.append(np.sqrt(2 / a) * np.sin(n * np.pi * x_vals / a))
        psi_derivs.append(np.sqrt(2) * np.pi * n * np.cos(np.pi * n * x_vals / a) / (a * np.sqrt(a)))
        psi_2nd_derivs.append(
            (np.sqrt(2) * np.pi ** 2 * n ** 2 * np.sin(np.pi * n * x_vals / a)) / (a ** 2 * np.sqrt(a)))
    else:
        psi_funcs.append(np.sqrt(2 / a) * np.cos(n * np.pi * x_vals / a))
        psi_derivs.append(-(np.sqrt(2) * np.pi * n * np.sin(np.pi * n * x_vals / a)) / (a * np.sqrt(a)))
        psi_2nd_derivs.append(
            (np.sqrt(2) * np.pi ** 2 * n ** 2 * np.cos(np.pi * n * x_vals / a)) / (a ** 2 * np.sqrt(a)))

print("======= expect_x =======")
expect_x_vals = []
for i in range(len(psi_funcs)):
    expect_x = np.sum(psi_funcs[i] * x_vals * psi_funcs[i]) * dx
    expect_x_vals.append(expect_x)
    print(f'expect_x_{i + 1} = {expect_x}')

print("======= expect_x^2 =======")
expect_x_sqrd_vals = []
for i in range(len(psi_funcs)):
    expect_x_sqrd = np.sum(psi_funcs[i] * x_vals ** 2 * psi_funcs[i]) * dx
    expect_x_sqrd_vals.append(expect_x_sqrd)
    print(f'expect_x^2_{i + 1} = {expect_x_sqrd}')

print("======= expect_p =======")
expect_p_vals = []
for i in range(len(psi_funcs)):
    expect_p = np.sum(psi_funcs[i] * 1j * hbar * psi_derivs[i]) * dx
    expect_p_vals.append(expect_p)
    print(f'expect_p_{i + 1} = {expect_p}')

print("======= expect_p^2 =======")
expect_p_sqrd_vals = []
for i in range(len(psi_funcs)):
    expect_p_sqrd = np.sum(psi_funcs[i] * hbar ** 2 * psi_2nd_derivs[i]) * dx
    expect_p_sqrd_vals.append(expect_p_sqrd)
    print(f'expect_p^2_{i + 1} = {expect_p_sqrd}')

print("======= sigma_x =======")
sigma_x_vals = []
for i in range(len(psi_funcs)):
    sigma_x = np.sqrt(expect_x_sqrd_vals[i] - expect_x_vals[i] ** 2)
    sigma_x_vals.append(sigma_x)
    print(f'sigma_x_{i + 1} = {sigma_x}')

print("======= sigma_p =======")
sigma_p_vals = []
for i in range(len(psi_funcs)):
    sigma_p = np.real(np.sqrt(expect_p_sqrd_vals[i] - expect_p_vals[i] ** 2))
    sigma_p_vals.append(sigma_p)
    print(f'sigma_p_{i + 1} = {sigma_p}')

print("======= uncertainty =======")
print(f'hbar/2 = {hbar / 2}')
for i in range(len(psi_funcs)):
    uncertainty = sigma_x_vals[i] * sigma_p_vals[i]
    print(f'sigma_x_{i + 1}*sigma_p_{i + 1} = {uncertainty}')