def main(argv):
if len(argv) > 1:
raise app.UsageError('Too many command-line arguments.')
logging.info(
'Solve Poschl-Teller potential with lambda=%f, scaling=%f',
FLAGS.lam, FLAGS.scaling)
logging.info(
'Number of electrons: %d', FLAGS.num_electrons)
logging.info(
'Grids: linspace(%f, %f, %d)',
FLAGS.grid_lower, FLAGS.grid_upper, FLAGS.num_grids)
exact_energy = single_electron.poschl_teller_eigen_energy(
level=FLAGS.num_electrons, lam=FLAGS.lam)
logging.info('Exact energy: %f', exact_energy)
logging.info('Solve with solver: %s', FLAGS.solver)
solver = getattr(single_electron, FLAGS.solver)(
grids=np.linspace(FLAGS.grid_lower, FLAGS.grid_upper, FLAGS.num_grids),
potential_fn=functools.partial(
single_electron.poschl_teller, lam=FLAGS.lam),
num_electrons=FLAGS.num_electrons)
solver.solve_ground_state()
logging.info('Numerical solution: %f', solver.total_energy)
logging.info('Difference: %e', solver.total_energy - exact_energy)
def test_poschl_teller_eigen_energy_float_lambda(self, level, lam,
expected_energy):
# NOTE(leeley): I calculated some eigen energy for float lambda by the
# expression in Phys. Rev. B 95, 115115
self.assertAlmostEqual(
single_electron.poschl_teller_eigen_energy(level, lam),
expected_energy)
def test_poschl_teller_eigen_energy_int_lambda(self, level, lam,
expected_energy):
# For integer value of lambda, the eigen energy is
# E = -\mu^2 / 2
# \mu = \lambda, \lambda - 1, ..., 1
# https://en.wikipedia.org/wiki/P%C3%B6schl%E2%80%93Teller_potential
self.assertAlmostEqual(
single_electron.poschl_teller_eigen_energy(level, lam),
expected_energy)