Thinking about photons as distinct from atomic Schroedinger solutions, is there significance to [J(J+1)] as the square of total angular momentum (AM)? We deal with photons as "spin-1" entities and this describes the transfer of a component of AM, I think in the propagation vector sense. I can see in atoms, massive systems, how there are components rendering a diffference between any chosen quantized "z-component", but is the commutative relation here between "Jz" and JTOTAL^2 relevant in photon analysis?

Photons are not described by solutions to the Schrödinger equation. Simply put, the Schrödinger equation is not Lorentz invariant.

 

What you need to look up are irreducible representations of the Poincare group and how they are labelled. For the photon you are interested in a massless representation.

 

Look up, Casimir operators, the Pauli-Lubanski tensor and helicity. Hope that helps.

Thanks ajb, I shall pursue what you are pointing to (Poynting to?)