RydbergStateMQDT

Class Methods

__init__(species, *[, nu, n, l, energy_au])	Initialize the Rydberg state.
calc_radial_matrix_element(other, k_radial)
copy()	Create a copy of the Rydberg state.
create_element(*[, use_nist_data])	Create the element for the Rydberg state.
create_grid([x_min, x_max, dz])	Create the grid object for the integration of the radial Schrödinger equation.
create_model([potential_type])	Create the model for the Rydberg state.
create_wavefunction([method, ...])
get_energy([unit])
get_label(fmt)	Label representing the ket.
get_n_star()	Calculate the effective quantum number n* for the Rydberg state.
sanity_check()	Check that the quantum numbers are valid.

Class Attributes and Properties

element	The element of the Rydberg state.
grid	The grid object for the integration of the radial Schrödinger equation.
model
nu	Return the effective quantum number nu = n*.
w_list	The list of w values for the wavefunction.
wavefunction
z_list	The list of z values for the grid.
species
n
l

class ryd_numerov.RydbergStateMQDT(species, *, nu=None, n=None, l=None, energy_au=None)

Initialize the Rydberg state.

Parameters:

• species (str) – Atomic species.

• nu (Optional[float]) – Effective principal quantum number of the rydberg electron, which is used to calculate the energy of the state.

• n (Optional[int]) – Principal quantum number of the rydberg electron.

• l (Optional[int]) – Orbital angular momentum quantum number of the rydberg electron.

• energy_au (Optional[float]) – The energy of the Rydberg state in atomic units (“hartree”). Either nu or energy_au must be provided.

species: str

n: Optional[int]

l: int

copy()

Create a copy of the Rydberg state.

Return type:

Self

get_label(fmt)

Label representing the ket.

Parameters:

fmt (Literal['raw', 'ket', 'bra']) – The format of the label, i.e. whether to return the raw label, or the label in ket or bra notation.

Return type:

str

Returns:

The label of the ket in the given format.

property nu: float

Return the effective quantum number nu = n*.

calc_radial_matrix_element(other, k_radial, unit=None)

Return type:

Union[PlainQuantity[float], float]

Parameters:

• other (Self)

• k_radial (int)

• unit (str | None)

create_element(*, use_nist_data=True)

Create the element for the Rydberg state.

Return type:

None

Parameters:

use_nist_data (bool)

create_grid(x_min=None, x_max=None, dz=0.01)

Create the grid object for the integration of the radial Schrödinger equation.

Parameters:

• x_min (Optional[float]) – The minimum value of the radial coordinate in dimensionless units (x = r/a_0). Default: Automatically calculate sensible value.

• x_max (Optional[float]) – The maximum value of the radial coordinate in dimensionless units (x = r/a_0). Default: Automatically calculate sensible value.

• dz (float) – The step size of the integration (z = r/a_0). Default: 1e-2.

Return type:

None

create_model(potential_type=None)

Create the model for the Rydberg state.

Parameters:

potential_type (Optional[Literal['coulomb', 'model_potential_marinescu_1993', 'model_potential_fei_2009']]) – Which potential to use for the model.

Return type:

None

create_wavefunction(method='numerov', sign_convention=None, *, run_backward=True, w0=1e-10, _use_njit=True)

Return type:

None

Parameters:

• method (Literal['numerov', 'whittaker'])

• sign_convention (Literal[None, 'positive_at_outer_bound', 'n_l_1'])

• run_backward (bool)

• w0 (float)

• _use_njit (bool)

property element: BaseElement

The element of the Rydberg state.

get_n_star()

Calculate the effective quantum number n* for the Rydberg state.

We define n* as :rtype: float

\[n^* = \sqrt{-\frac{1}{2} \frac{\mu}{E} }\]

where mu = R_M/R_infty is the reduced mass and E the energy of the state.

Return type:

float

property grid: Grid

The grid object for the integration of the radial Schrödinger equation.

property model: Model

sanity_check()

Check that the quantum numbers are valid.

Return type:

None

property w_list: ndarray[tuple[int, ...], dtype[Any]]

The list of w values for the wavefunction.

property wavefunction: Wavefunction

property z_list: ndarray[tuple[int, ...], dtype[Any]]

The list of z values for the grid.

get_energy(unit=None)

Return type:

Union[PlainQuantity[float], float]

Parameters:

unit (str | None)