A Note on Orbital and Spin Angular Momenta

Gianluca Stefanucci

K. Heyde, John L. Wood

M. I. Krivoruchenko

The Frobenius covariant is used to construct a projection operator onto the spin-S eigenspaces associated with the squares of the total and orbital angular momenta. The covariant admits two equivalent representations: as a polynomial in powers of the scalar product of the spin and orbital angular momentum operators, and as a finite expansion in terms of their respective polarization operators. A correspondence is established with Villars' angular momentum projection, used in nuclear structure studies.

A. C. Sharma

This chapter covers various aspects of orbital, total, and spin angular momenta and the Clebsch-Gordon coefficients. An approach that is not found in many books, is used to derive eigenvalues of orbital angular momentum. The Pauli theory of spin half systems, addition of angular momenta, eigenfunctions of orbital angular momentum, computation of Clebsch-Gordon coefficients, solved examples, and unsolved exercises are included in the chapter. The basic purpose of the chapter has been to bring out the quantum mechanical importance of the theory of angular momenta with the use of essential mathematical derivations, which are self-consistent, and to adopt an elegant modern approach. Special mention on why orbital angular momentum cannot have non-integer values is made. The concept of spin angular momentum, which is purely a quantum mechanical quantity, is introduced in a simple and most convincing manner.

Fam Le Kien, Thomas Busch

We calculate analytically and numerically the axial orbital and spin torques of guided light on a two-level atom near an optical nanofiber. We show that the generation of these torques is governed by the angular momentum conservation law in the Minkowski formulation. The orbital torque on the atom near the fiber has a contribution from the average recoil of spontaneously emitted photons. Photon angular momentum and atomic spin angular momentum can be converted into atomic orbital angular momentum. The orbital and spin angular momenta of the guided field are not transferred separately to the orbital and spin angular momenta of the atom.

P. T. Leung