Example2.py

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import numpy as np
import matplotlib.pyplot as plt
from pyhamsys import HamSys, Parameters

## Parameters
potential = lambda x: -1 / np.sqrt(x**2 + 1)
psi0 = lambda x: np.exp(-x**2 / 50)
tf, timestep = 5e1, 1e-2
L, N = 100, 2**10

## Intermediate variables
xgrid = np.linspace(-L, L, N, endpoint=False, dtype=np.float64)
vgrid = potential(xgrid).astype(np.complex128)
dx = xgrid[1] - xgrid[0]

## Hamiltonian system and equations of motion
def y_dot(t, psi):
	psi_, _psi = np.roll(psi, 1), np.roll(psi, -1)
	lap_psi = (psi_ + _psi - 2 * psi) / dx**2
	return -1j * (-lap_psi / 2 + vgrid * psi) 

hs = HamSys(ndof=N, btype='psi', y_dot=y_dot)

## Integration and plot of wavefunction
plt.ion()
fig, ax = plt.subplots()
h, = ax.plot(xgrid, np.abs(psi0(xgrid))**2, color='#003366', linewidth=2)
ax.set_title('$t = 0 $', loc='right', pad=20)
ax.set_xlabel('$x$')
ax.set_ylabel(r'$\vert\psi (x,t)\vert^2$')
ax.set_ylim((-0.1, 3.5))

def plot(t, psi):
	if (int(t / timestep) + 1) % 50 == 0:
		h.set_ydata(np.abs(psi)**2)
		ax.set_title(f'$t = {{{t:.1f}}}$', loc='right', pad=20)
		plt.pause(1e-4)
		
sol = hs.integrate(psi0(xgrid), (0, tf), params=Parameters(step=timestep, extension=True), command=plot)

plt.ioff()
plt.show()