import numpy as np

a = 1
hbar = 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 =======")
for i in range(len(psi_funcs)):
    expect_x = np.sum(psi_funcs[i] ** 2 * x_vals) * dx
    print(f'expect_x_{i + 1} = {expect_x}')

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

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

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