On The Harmonic Oscillator Group

Details On The Harmonic Oscillator Group On The Harmonic Oscillator Group

2011-11-23

arxiv.org/abs/1111.5569v2

Physics

Mathematical Physics

11 pages, no figures

Scientific paper

We discuss the maximum kinematical invariance group of the quantum harmonic oscillator from a view point of the Ermakov-type system. A six parameter family of the square integrable oscillator wave functions, which seems cannot be obtained by the standard separation of variables, is presented as an example. The invariance group of generalized driven harmonic oscillator is shown to be isomorphic to the corresponding Schroedinger group of the free particle.

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