Bohr-Sommerfeld Quantization of Pseudospin Hamiltonians

Abstract

It is shown here how to map the problem with pseudospin $J$ into an equivalent one in which $\frac{1}{J}$ plays the role of $\hslash$ and canonical variables exist at the classical level. Bohr-Sommerfeld quantization of the equivalent theory is found to produce a spectrum in very good agreement with the exact results for the Lipkin-Meshkov-Glick model at $J=15\mathrm{} \mathrm{and} 25$. The method readily extends to the $\mathrm{SU}\mathrm{}\left(n\right)\mathrm{}$ case.