A note on the angular momentum operators

P. T. Leung

B. G. Wybourne, Lidia Smentek

M. Leichter

Nazakat Ullah

It is shown that angular momentum operator identities between ladder operators and rotation operators can be used to study the trace problem. Using an explicit representation of the rotation matrices, the author evaluates the trace of the operator ${J}_{\ensuremath{-}}^{k}{J}_{+}^{k}$ in closed form. The identities are found to be particularly useful in providing checks for the sum of the traces.