Amplitude and phase representation of quantum invariants for the time dependent harmonic oscillator

Details Amplitude and phase representation of quantum invariants for the time dependent harmonic oscillator Amplitude and phase representation of quantum invariants for the time dependent harmonic oscillator

2002-12-12

arxiv.org/abs/quant-ph/0212073v1

Physics

Quantum Physics

Scientific paper

10.1103/PhysRevA.67.063803

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.

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