Generalized Angular Momentum

Generalized angular momentum is defined by generalizing commutation relations satisfied by Cartesian components of orbital angular momentum. Its properties and eigen value solutions are obtained algebraically. Quantum number \(\hskip 0.05cm j \hskip 0.05cm\) , associated with eigen value \(j(j+1)\hbar ^2\) of \(\widehat {J}^{2}\) , is shown to admit only non-negative integral or half-odd-integral values. \(j={\frac {1}{2}}\) can be associated with intrinsic magnetic moment and spin of the electron. Isospin of nucleons is introduced by analogy. Matrix representation and matrix elements of angular momenta are obtained.