Wavefunction

Class Methods

__init__(state, grid)	Create a Wavefunction object.
apply_sign_convention(sign_convention)	Set the sign of the wavefunction according to the sign convention.
integrate()	Integrate the radial Schrödinger equation and store the wavefunction in the w_list attribute.

Class Attributes and Properties

nodes	The number of nodes (i.e. zero-crossings) of the wavefunction.
r_list	The radial wavefunction tilde{R}(r) in atomic units tilde{R}(r) = a_0^{-3/2} R(r).
u_list	The dimensionless wavefunction tilde{u}(x) = sqrt(a_0) r R(r).
w_list	The dimensionless scaled wavefunction w(z) = z^{-1/2} tilde{u}(x=z^2) = (r/a_0)^{-1/4} sqrt(a_0) r R(r).

class ryd_numerov.radial.Wavefunction(state, grid)

Create a Wavefunction object.

Parameters:

• state (RydbergStateBase) – The RydbergState object.

• grid (Grid) – The grid object.

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

The dimensionless scaled wavefunction w(z) = z^{-1/2} tilde{u}(x=z^2) = (r/a_0)^{-1/4} sqrt(a_0) r R(r).

property u_list: ndarray[tuple[Any, ...], dtype[Any]]

The dimensionless wavefunction tilde{u}(x) = sqrt(a_0) r R(r).

property r_list: ndarray[tuple[Any, ...], dtype[Any]]

The radial wavefunction tilde{R}(r) in atomic units tilde{R}(r) = a_0^{-3/2} R(r).

property nodes: int

The number of nodes (i.e. zero-crossings) of the wavefunction.

abstract integrate()

Integrate the radial Schrödinger equation and store the wavefunction in the w_list attribute.

Return type:

None

apply_sign_convention(sign_convention)

Set the sign of the wavefunction according to the sign convention.

Parameters:

sign_convention (Literal[None, 'positive_at_outer_bound', 'n_l_1']) – The sign convention for the wavefunction. - None: Leave the wavefunction as it is. - “n_l_1”: The wavefunction is defined to have the sign of (-1)^{(n - l - 1)} at the outer boundary. - “positive_at_outer_bound”: The wavefunction is defined to be positive at the outer boundary.

Return type:

None