f-Oscillators and Nonlinear Coherent States

Details f-Oscillators and Nonlinear Coherent States f-Oscillators and Nonlinear Coherent States

1996-11-30

arxiv.org/abs/quant-ph/9612006v1

Phys.Scripta55:528,1997

Physics

Quantum Physics

Latex, 32 pages, accepted by Physica Scripta

Scientific paper

10.1088/0031-8949/55/5/004

The notion of f-oscillators generalizing q-oscillators is introduced. For classical and quantum cases, an interpretation of the f-oscillator is provided as corresponding to a special nonlinearity of vibration for which the frequency of oscillation depends on the energy. The f-coherent states (nonlinear coherent states) generalizing q-coherent states are constructed. Applied to quantum optics, photon distribution function, photon number means, and dispersions are calculated for the f-coherent states as well as the Wigner function and Q-function. As an example, it is shown how this nonlinearity may affect the Planck distribution formula.

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