qm_sim.temporal_solver.crank_nicolson.CrankNicolson

class qm_sim.temporal_solver.crank_nicolson.CrankNicolson(H: Callable[[float], ndarray], output_shape: tuple[int] = None)

Bases: TemporalSolver

__init__(H: Callable[[float], ndarray], output_shape: tuple[int] = None)

Initialize a temporal solver

Parameters:

• H (Callable[[float], np.ndarray]) – Function of time, representing the temporal derivative at that time

• output_shape (tuple[int], optional) – Expected shape of the solution, defaults to None

Methods

__init__(H[, output_shape])	Initialize a temporal solver
iterate(v_0, t0, t_final, dt[, dt_storage, ...])	Iterate the time propagation scheme.
tqdm(t_start, t_end, enable)

Attributes

explicit	Is the method explicit or implicit?
name	Name of the solver
order	Integration order
stable	Is the method stable? If only conditionally stable, this will be true and dt will be forced into its stable range

explicit: bool = False

Is the method explicit or implicit?

iterate(v_0: ndarray, t0: float, t_final: float, dt: float, dt_storage: float = None, verbose: bool = True) → tuple[ndarray, ndarray]

Iterate the time propagation scheme. Store the current state every dt_storage

Args:

t_final (float):

End time for calculations

dt_storage (float, optional):

Data storage period. If None, store each calculation dt Defaults to None.

Returns:

np.ndarray:

Time values, shape (n,) for n storage times

np.ndarray:

State at times stored in the other output. shape (n, H.shape)

name: str = 'crank-nicolson'

Name of the solver

order: int = 2

Integration order

stable: bool = True

Is the method stable? If only conditionally stable, this will be true and dt will be forced into its stable range