Amplitude and phase representation of quantum invariants for the time-dependent harmonic oscillator
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.
arXiv:quant-ph/0212073•Physical Review A•Jun 11, 2003•28 citations