exatomic.algorithms.harmonics module

Spherical and Solid Harmonics

These functions generate and manipulate spherical and solid harmonics. For solid harmonics, this module provides numerical approaches for dealing with them.

class exatomic.algorithms.harmonics.SolidHarmonics

Bases: object

Store a collection of solid harmonic functions.

exatomic.algorithms.harmonics.solid_harmonics(l, return_all=False, vectorize=False, standard_symbols=True)

Generate a set of spherical solid harmonic functions for a given angular momentum.

>>> solid_harmonics(0)
{(0, 0): 1}
>>> solid_harmonics(1, True)
{(0, 0): 1, (1, 1): x, (1, -1): y, (1, 0): z}

Parameters:

• l (int) – Orbital angular moment

• return_all (bool) – If true, return all computed solid harmonics

• vectorize (bool) – If true, return vectorized functions (for numerical methods)

• standard_symbols (bool) – If true (default), convert to standard symbol notation (e.g. x*y => xy)

Returns:

functions (dict) – Dictionary of (l, ml) keys and symbolic function values