pauli.m

Pauli matrices (sparse, see below for normalisation conventions) for a spin of a user-specified energy level multiplicity.

Syntax

    S=pauli(mult)

Arguments

    mult - an integer specifying the 
           multiplicity of the spin

Outputs

    S.u - unit operator

    S.p - raising operator

    S.m - lowering operator

    S.x - Sx observable operator

    S.y - Sy observable operator

    S.z - Sz observable operator

Notes

1. The matrices are normalized so as to obey the following commutation relations:

         [S.x,S.y]=1i*S.z
         [S.y,S.z]=1i*S.x
         [S.z,S.x]=1i*S.y

2. Raising and lowering operators are defined as:

          S.p=S.x+1i*S.y
          S.m=S.x-1i*S.y

3. It is never a good idea to normalise spin operators using matrix norms because commutation relations would break.

See also

stevens.m, irr_sph_ten.m, wigner.m, operator.m, state.m, hamiltonian.m

SU(2), SO(3), and other groups

Version 2.8, authors: Ilya Kuprov