Irreducible spherical tensor operators.

T = isto(S,[k,q])
T = isto(S,[k,q,iSpin])
T = isto(___,'sparse')

This function provides matrix representations of the irreducible spherical tensor operator (ISTO) components for a spin, or set of spins, with quantum number(s) S. S can be a single quantum number, or an array of quantum numbers representing a spin system. It can also be a spin system.

The parameters k and q specify the operator component. Allowed values are 0<=k<=2S and q=-k,...,k. k is the rank of the operator, and q is the component. For a multi-spin system, both k and q need to be column vectors, with one entry for each spin in S. As an alternative, a third column of spin indices can be provided. In this cases, k and q are used for the spins with indices in i, and for all other spins it is assumed that both k and q are zero.

Including 'sparse' as the last argument instructs isto() to return the matrix in sparse format, and not in full format.

The ISTO component (2,1) for a spin 3/2 is

isto(3/2,[2 1])

    ans =
    0      -1.7321            0            0
    0            0            0            0
    0            0            0       1.7321
    0            0            0            0

To get an ISTO for a system of three spins-3/2 with k=2 and q=-1 for the third spin, and zero for all others, use one of two following ways

S = [1 1 1];
isto(S,[2 -1 3])
isto(S,[0 0; 0 0; 2 1])

The operator matrices are computed using Racah's commutation rule. See I.D.Ryabov, J.Magn.Reson. 140, 141-145 (1999).

spin operators, sop, stev