Quantum phase and a<i>q</i>-deformed quantum oscillator

Abstract

The q-deformed quantum oscillator for q=${\mathit{e}}^{\mathit{i}2\mathrm{\ensuremath{\pi}}/(\mathit{s}+1)}$ has reducible representations that admit unitary phase operators. In the classical limit s\ensuremath{\rightarrow}\ensuremath{\infty}, of zero deformation, they provide the phase angles of the ordinary quantum oscillator. The formalism is applied to the master equation of a q-deformed laser mode that is introduced and solved in the steady state and then used to evaluate the statistical moments of the cosine and sine operators.