Algebraic Treatment of PT-Symmetric Coupled Oscillators

Abstract

The purpose of this paper is the discussion of a pair of coupled linear oscillators that has recently been proposed as a model of a system of two optical resonators. By means of an algebraic approach we show that the frequencies of the quantum-mechanical interpretation of the optical phenomenon are linear combinations of the classical frequencies. Consequently, if the classical frequencies are real, then the quantum-mechanical eigenvalues are also real.