AngularState

Class Methods

__init__(coefficients, kets)
calc_exp_qn(q)	Calculate the expectation value of a quantum number q.
calc_matrix_element(other, operator, kappa, q)	Calculate the dimensionless angular matrix element.
calc_reduced_matrix_element(other, operator, ...)	Calculate the reduced angular matrix element.
calc_reduced_overlap(other)	Calculate the reduced overlap <self||other> (ignoring the magnetic quantum number m).
calc_std_qn(q)	Calculate the standard deviation of a quantum number q.
to(coupling_scheme)	Convert to specified coupling scheme.

Class Attributes and Properties

coefficients	Return the coefficients as numpy array.
coupling_scheme	Return the coupling scheme of the state.
f_tot	Return the total f quantum number of the state.
i_c	Return the i_c quantum number of the state.
m	Return the m quantum number of the state.
norm	Return the norm of the state (should be 1).
parity	Return the parity of the state.

class rydstate.angular.AngularState(coefficients, kets)

Parameters:

• coefficients (Sequence[float] | NDArray)

• kets (Sequence[GenericT_AngularKet])

property coupling_scheme: Literal['LS', 'JJ', 'FJ']

Return the coupling scheme of the state.

property norm: float

Return the norm of the state (should be 1).

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

Return the coefficients as numpy array.

property i_c: float

Return the i_c quantum number of the state.

property f_tot: float

Return the total f quantum number of the state.

property parity: int

Return the parity of the state.

property m: float | NotSet

Return the m quantum number of the state.

to(coupling_scheme)

Convert to specified coupling scheme.

Overloads:

• self, coupling_scheme (Literal[‘LS’]) → AngularState[AngularKetLS[Any]]

• self, coupling_scheme (Literal[‘JJ’]) → AngularState[AngularKetJJ[Any]]

• self, coupling_scheme (Literal[‘FJ’]) → AngularState[AngularKetFJ[Any]]

Parameters:

• coupling_scheme (Literal['LS', 'JJ', 'FJ']) – The coupling scheme to convert to (e.g. “LS”, “JJ”, “FJ”).

• self (AngularState[Any])

Returns:

The angular state in the specified coupling scheme.

Return type:

AngularState[Any]

calc_exp_qn(q)

Calculate the expectation value of a quantum number q.

Parameters:

q (Literal['i_c', 's_c', 'l_c', 's_r', 'l_r', 's_tot', 'l_tot', 'j_c', 'j_r', 'j_tot', 'f_c', 'f_tot']) – The quantum number to calculate the expectation value for.

Return type:

float

calc_std_qn(q)

Calculate the standard deviation of a quantum number q.

Parameters:

q (Literal['i_c', 's_c', 'l_c', 's_r', 'l_r', 's_tot', 'l_tot', 'j_c', 'j_r', 'j_tot', 'f_c', 'f_tot']) – The quantum number to calculate the standard deviation for.

Return type:

float

calc_reduced_overlap(other)

Calculate the reduced overlap <self||other> (ignoring the magnetic quantum number m).

Return type:

float

Parameters:

other (AngularState[Any] | AngularKetBase[Any])

calc_reduced_matrix_element(other, operator, kappa)

Calculate the reduced angular matrix element.

This means, calculate the following matrix element (self is the bra, other is the ket):

\[\left\langle self || \hat{O}^{(\kappa)} || other \right\rangle\]

Parameters:

• other (Union[AngularState[Any], AngularKetBase[Any]]) – The other AngularState (or AngularKet) \(|other>\) (used as the ket).

• operator (Literal['spherical', 'i_c', 's_c', 'l_c', 's_r', 'l_r', 's_tot', 'l_tot', 'j_c', 'j_r', 'j_tot', 'f_c', 'f_tot', 'identity_i_c', 'identity_s_c', 'identity_l_c', 'identity_s_r', 'identity_l_r', 'identity_s_tot', 'identity_l_tot', 'identity_j_c', 'identity_j_r', 'identity_j_tot', 'identity_f_c', 'identity_f_tot']) – The operator type \(\hat{O}^{(\kappa)}\) for which to calculate the matrix element. E.g. ‘spherical’, ‘s_tot’, ‘l_r’, etc.

• kappa (int) – The rank \(\kappa\) of the angular momentum operator.

• self (Self)

Return type:

float

Returns:

The reduced dimensionless angular matrix element.

calc_matrix_element(other, operator, kappa, q)

Calculate the dimensionless angular matrix element.

This means, calculate the following matrix element (self is the bra, other is the ket):

\[\left\langle self | \hat{O}^{(\kappa)}_q | other \right\rangle\]

Parameters:

• other (Union[AngularState[Any], AngularKetBase[Any]]) – The other AngularState (or AngularKet) \(|other>\) (used as the ket).

• operator (Literal['spherical', 'i_c', 's_c', 'l_c', 's_r', 'l_r', 's_tot', 'l_tot', 'j_c', 'j_r', 'j_tot', 'f_c', 'f_tot', 'identity_i_c', 'identity_s_c', 'identity_l_c', 'identity_s_r', 'identity_l_r', 'identity_s_tot', 'identity_l_tot', 'identity_j_c', 'identity_j_r', 'identity_j_tot', 'identity_f_c', 'identity_f_tot']) – The operator type \(\hat{O}^{(\kappa)}_q\) for which to calculate the matrix element. E.g. ‘spherical’, ‘s_tot’, ‘l_r’, etc.

• kappa (int) – The rank \(\kappa\) of the angular momentum operator.

• q (int) – The component \(q\) of the angular momentum operator.

• self (Self)

Return type:

float

Returns:

The dimensionless angular matrix element.