def test_cn_delta():
depths = [0.2, 1.0, 5.0]
for d in depths:
v = potential.DeltaPotential1D(d)
e0 = v.get_eigenenergy()
tmax = -2 * np.pi / e0
dt = tmax / 500
s = solver.CrankNicolsonSolver(20 / d, 0.1 / d, dt, v)
psi0 = v.get_eigenfunction()
psi0_value = psi0(s.x)
np.testing.assert_almost_equal(wavefunction.norm(s.x, psi0_value),
1,
decimal=2)
times = [tmax, tmax / 2, tmax / 4]
psi_expected = [
psi0_value, -psi0_value, psi0_value * np.exp(0.5j * np.pi)
]
for t, psi1 in zip(times, psi_expected):
psi = s.execute(t, psi0=psi0)
np.testing.assert_almost_equal(
wavefunction.norm(s.x, psi),
wavefunction.norm(s.x, psi0_value),
decimal=7,
err_msg=f"Norm not conserved for depth {d}")
np.testing.assert_allclose(np.abs(psi),
np.abs(psi0_value),
atol=0.02)
np.testing.assert_allclose(psi, psi1, atol=0.05)
def test_euler_delta():
depths = [0.2, 1.0, 5.0]
for d in depths:
v = potential.DeltaPotential1D(d)
e0 = v.get_eigenenergy()
tmax = -2 * np.pi / e0
dt = tmax / 500000
s = solver.EulerSolver(20 / d, 0.1 / d, dt, v)
psi0 = v.get_eigenfunction()
psi0_value = psi0(s.x)
np.testing.assert_almost_equal(wavefunction.norm(s.x, psi0_value),
1,
decimal=2)
psi = s.execute(tmax, psi0=psi0)
np.testing.assert_almost_equal(
wavefunction.norm(s.x, psi),
wavefunction.norm(s.x, psi0_value),
decimal=3,
err_msg=f"Norm not conserved for depth {d}")
np.testing.assert_allclose(np.abs(psi), np.abs(psi0_value), atol=0.06)
def test_delta_potential():
x = np.linspace(-50, 50, 40000)
depths = np.linspace(0.1, 10, 10)
for d in depths:
v = potential.DeltaPotential1D(d)
assert (v.get_delta_depth() == d)
assert (v.get_number_of_levels() == 1)
with pytest.raises(ValueError):
v.get_eigenenergy(random.randint(1, 100))
with pytest.raises(ValueError):
v.get_eigenfunction(random.randint(1, 100))
psi = v.get_eigenfunction()(x)
np.testing.assert_almost_equal(wavefunction.norm(x, psi),
1.0,
decimal=4,
err_msg=f"Norm is not 1 for depth {d}")
def test_uniform_field():
amps = [1.0, -2.0, lambda t: 0.5 * t]
t = 3.0
x = np.linspace(-10, 10, 1000)
for amp in amps:
v = potential.UniformField1D(amp)
assert (v.get_number_of_levels() == 0)
with pytest.raises(ValueError):
v.get_eigenfunction()
with pytest.raises(ValueError):
v.get_eigenenergy()
if callable(amp):
np.testing.assert_allclose(-amp(t) * x, v.get_potential()(t, x))
else:
np.testing.assert_allclose(-amp * x, v.get_potential()(x))
assert (v.get_delta_depth() == 0.0)
v = potential.UniformField1D(
amp, potential=potential.QuadraticPotential1D(1.0))
if callable(amp):
value1 = -amp(t) * x + 0.5 * x**2
value2 = v.get_potential()(t, x)
else:
value1 = -amp * x + 0.5 * x**2
value2 = v.get_potential()(x)
np.testing.assert_allclose(value1, value2)
v = potential.UniformField1D(amp,
potential=potential.DeltaPotential1D(1.0))
if callable(amp):
np.testing.assert_allclose(-amp(t) * x, v.get_potential()(t, x))
else:
np.testing.assert_allclose(-amp * x, v.get_potential()(x))
assert (v.get_delta_depth() == 1.0)
def test_sohs_non_stationary_delta():
_test_non_stationary(solver.SplitOperatorHalfSpectralSolver,
potential.DeltaPotential1D(1.0))
def test_cn_non_stationary_delta():
_test_non_stationary(solver.CrankNicolsonSolver,
potential.DeltaPotential1D(1.0))