equitorch.constants

Defines mathematical constants and utility functions.

equitorch.constants.j_matrix(l: int)

Computes the Wigner D-matrix for the rotation that exchanges y-z axes and reverses x-axis.

This function calculates the Wigner D-matrix corresponding to a specific rotation transformation that exchanges the y and z axes while reversing the direction of the x-axis. It is used in general Wigner D-matrix calculations.

Parameters:

l – The angular momentum quantum number.

Returns:

The Wigner D-matrix for the specified rotation transformation.

Return type:

sympy.Matrix

equitorch.constants.so3_clebsch_gordan(l, l1, l2)

Computes the Clebsch-Gordan coefficients for SO(3) group.

This function calculates the Clebsch-Gordan coefficients for the SO(3) group, which are used to decompose the tensor product of two irreducible representations into a direct sum of irreducible representations.

Parameters:

• l – An integer representing the angular momentum quantum number of the resulting representation.

• l1 – An integer representing the angular momentum quantum number of the first representation.

• l2 – An integer representing the angular momentum quantum number of the second representation.

Returns:

The Clebsch-Gordan coefficients matrix for the specified angular momenta.

Return type:

sympy.Array