Generalized Angular Momentum and the Coupling of Angular Momenta

Qingchun Zhou

Based on the properties of angular momentum, the paper gives the general matrix form of operator J 1 J 2 in non-coupling representation, proposes a method for finding vector-coupling coefficients of two angular momenta by solving linear simultaneous equations, then an example is provided to demonstrate the simplicity of the method.

Stephen P. Martin

Walter Wilcox

Synopsis: General operator properties of angular momenta are recalled, and a physical motivation for adding them is given. The product and total angular momentum bases are defined. It is shown how to express one basis in terms of the other, and an explicit example of adding two spin 1/2 angular momenta is given. A further example consists of adding a general orbital angular momentum value to spin 1/2. These considerations are applied to perturbations in the hydrogen atom energy spectrum, where the correct choice for calculations is the total angular momentum basis.

Walter Wilcox

Synopsis: General operator properties of angular momenta are recalled, and a physical motivation for adding them is given. ƒe product and total angular momentum bases are defined. It is shown how to express one basis in terms of the other, and an explicit example of adding two spin 1/2 angular momenta is given. A further example consists of adding a general orbital angular momentum value to spin 1/2. ƒese considerations are applied to perturbations in the hydrogen atom energy spectrum, where the correct choice for calculations is the total angular momentum basis.

Alvin Meckler