def test_spf(spf_2dho):
n, l, radius, num_grid_points, spf_test = spf_2dho
tdho = TwoDimensionalHarmonicOscillator(n, l, radius, num_grid_points)
tdho.setup_spf()
for p in range(l // 2):
np.testing.assert_allclose(spf_test[p], tdho.spf[p])
def test_two_body_elements_compare():
n = 2
l = 6
grid_length = 5
num_grid_points = 201
mass = 1
omega = 1
omega_c = 0
two_dim_ho = GeneralOrbitalSystem(
n,
TwoDimensionalHarmonicOscillator(
l, grid_length, num_grid_points, mass=mass, omega=omega
),
)
two_dim_ho_b = GeneralOrbitalSystem(
n,
TwoDimHarmonicOscB(
l,
grid_length,
num_grid_points,
mass=mass,
omega=omega,
omega_c=omega_c,
),
)
np.testing.assert_allclose(two_dim_ho.u, two_dim_ho_b.u, atol=1e-8)
def test_change_of_basis():
# We try to construct a two-dimensional double-well system from a
# two-dimensional harmonic oscillator system by using the change-of-basis
# function with C found from diagonalizing the double-well one-body
# Hamiltonian.
n = 2
l = 12
omega = 1
mass = 1
barrier_strength = 3
radius = 10
num_grid_points = 401
axis = 0
tdho = GeneralOrbitalSystem(
n,
TwoDimensionalHarmonicOscillator(
l, radius, num_grid_points, omega=omega
),
)
h_dw = get_double_well_one_body_elements(
l, omega, mass, barrier_strength, dtype=np.complex128, axis=axis
)
epsilon, C_dw = np.linalg.eigh(h_dw)
C = BasisSet.add_spin_one_body(C_dw, np=np)
tdho.change_basis(C)
tddw = GeneralOrbitalSystem(
n,
TwoDimensionalDoubleWell(
l,
radius,
num_grid_points,
omega=omega,
mass=mass,
barrier_strength=barrier_strength,
axis=axis,
),
)
tddw.change_basis(C)
np.testing.assert_allclose(tdho.u, tddw.u, atol=1e-7)
np.testing.assert_allclose(tdho.spf, tddw.spf, atol=1e-7)
def test_zero_barrier():
"""Test checking if we can reproduce the regular two-dimensional harmonic
oscillator system when setting the barrier strength to zero.
"""
n = 2
l = 12
radius = 10
num_grid_points = 401
tddw = TwoDimensionalDoubleWell(
l, radius, num_grid_points, barrier_strength=0, axis=0
)
tdho = TwoDimensionalHarmonicOscillator(l, radius, num_grid_points)
np.testing.assert_allclose(tddw.h, tdho.h, atol=1e-7)
np.testing.assert_allclose(tddw.u, tdho.u, atol=1e-7)
np.testing.assert_allclose(tddw.spf, tdho.spf, atol=1e-7)
import numpy as np
from matplotlib import cm
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
from quantum_systems import TwoDimensionalHarmonicOscillator
n = 2
l = 30
radius_length = 4
num_grid_points = 101
tdho = TwoDimensionalHarmonicOscillator(n, l, radius_length, num_grid_points)
tdho.setup_spf()
fig = plt.figure(figsize=(16, 12))
fig.suptitle(r"Probability density $\langle \phi_p \vert \phi_p \rangle$")
for p in range(l // 2):
ax = fig.add_subplot(3, 5, p + 1, polar=True)
ax.set_title(fr"$p = {p}$", loc="left")
plt.contourf(tdho.T, tdho.R,
np.abs(tdho.spf[2 * p] * tdho.spf[2 * p].conj()))
fig = plt.figure(figsize=(16, 12))
fig.suptitle(r"$\Re(\phi_p(\mathbf{r}))^2$")
for p in range(l // 2):
ax = fig.add_subplot(3, 5, p + 1, polar=True)
ax.set_title(fr"$p = {p}$", loc="left")
import numpy as np
import matplotlib.pyplot as plt
from quantum_systems import TwoDimensionalHarmonicOscillator
n = 2
l = 30
radius_length = 4
num_grid_points = 101
tdho = TwoDimensionalHarmonicOscillator(n, l, radius_length, num_grid_points)
tdho.construct_dipole_moment()
plt.subplot(2, 2, 1)
plt.imshow(tdho.dipole_moment[0].real)
plt.title(r"$\Re(\langle p | \hat{x} | q \rangle)$")
plt.xlabel(r"$q$")
plt.ylabel(r"$p$")
ax = plt.gca()
ax.set_xticks(np.arange(0, l))
ax.set_yticks(np.arange(0, l))
ax.set_xticklabels(np.arange(0, l))
ax.set_yticklabels(np.arange(0, l))
ax.set_xticks(np.arange(-0.5, l - 0.5), minor=True)
ax.set_yticks(np.arange(-0.5, l - 0.5), minor=True)
ax.grid(which="minor", color="w", linewidth=1)