Phase operator for the harmonic oscillator

E. C. Lerner

E. C. Lerner

Kumar Eswaran

Gavriel Segre

After a brief introduction recalling how, in the limit in which the mass and the electric charge of the electron and the positron tend to zero, Quantum Electrodynamics reduces to a collection of uncoupled quantum supersymmetric harmonic oscillators, the phase operator of the quantum fermionic harmonic oscillator and of the quantum supersymmetric harmonic oscillator are introduced and their properties analyzed. It is then shown that the phase operator of a supersymmetric harmonic oscillator is a Goldstone operator at any strictly positive temperature (finite or infinite).

M. Fernández‐Guasti, H. M. Moya-Cessa

The correspondence between classical and quantum invariants is established. The Ermakov-Lewis quantum invariant of the time-dependent harmonic oscillator is translated from the coordinate and momentum operators into amplitude and phase operators. In doing so, Turski's phase operator as well as Susskind-Glogower operators are generalized to the time-dependent harmonic-oscillator case. A quantum derivation of the Manley-Rowe relations is shown as an example.

Laurent A. Beauregard