# Sle operators.m

From Spinach Documentation Wiki

Wigner D function basis set and rotation generators required by the gridfree.m context.

## Syntax

[Lx,Ly,Lz,D,space_basis]=sle_operators(max_rank)

## Description

The function returns matrix representations of the angular momentum operators in the basis of Wigner D functions, matrix representations of Wigner D function product operators, and a descriptor of the basis itself.

## Arguments

max_rank - maximum L rank for Wigner D functions

## Returns

space_basis - lab space basis set descriptor, in [L M N] format, giving indices of each Wigner function in the basis. Lx,Ly,Lz - representations of lab space rotation generators in the Wigner function basis, to be used in the building of the lab space diffusion operator. D - a cell array of Wigner function product superoperators, corresponding to multi- plication by D[2,M,N] of the basis Wig- ner functions, to be used in the build- ing of the spin Hamiltonian operator.

## Examples

This function is used by gridfree.m context to generate the spatial basis. All SLE calculations and grid-free powder NMR calculations use that context.

## Notes

Automatic caching is implemented - the function would not recompute operator sets that it can find on disk.

## See also

wigner.m, gridfree.m, v2fplanck.m, irr_sph_ten.m, clebsch_gordan.m, wigner_3j.m, wigner_6j.m

*Version 1.10, authors: Luke Edwards, Ilya Kuprov*