import numpy as np
import pylab as pl
from scipy.optimize import fsolve


def cot(x):
    return 1 / np.tan(x)


a = 5
hbar = 1
m = 1
z = 2.851
l = z / a
V0 = 2
D = 1

x = np.linspace(-10, 10, 1000)
x_pos = x[x > 0]
z0 = (a / hbar) * np.sqrt(2 * m * V0)
print(f'z0 = {z0}')
k = -l * cot(l * a)


# Define the functions for the wavefunction and its derivative
def psi_inside(x):
    return D * np.sin(l * x)


def psi_outside(x, F):
    return F * np.exp(-k * x)


def dpsi_inside(x):
    return D * l * np.cos(l * x)


def dpsi_outside(x, F):
    return -F * k * np.exp(-k * x)


# Define the equations for the continuity conditions
def equations(p):
    return psi_inside(a) - psi_outside(a, p)


# Solve for D and F
F = fsolve(equations, np.ndarray(1))
print(f'F = {F}')

psi_conditions = [
    (0 < x_pos) & (x_pos <= a),
    (x_pos > a)
]
psi_funcs = [
    lambda x: psi_inside(x),
    lambda x: psi_outside(x, F),
]
psi_half = np.piecewise(x_pos, psi_conditions, psi_funcs)
psi = np.concatenate((-np.flip(psi_half), psi_half))

V0_graph = np.piecewise(x, [(x < -a), (-a <= x) & (x <= a), (x > a)], [0, -V0, 0])

pl.plot(x, psi)
pl.plot(x, V0_graph)
pl.show()