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arXiv · quant-ph/9612006

f-Oscillators and Nonlinear Coherent States

V. I. Man'ko·G. Marmo·E. C. G. Sudarshan·F. Zaccaria
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Abstract

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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V. I. Man'ko, G. Marmo, E. C. G. Sudarshan, F. Zaccaria. 1996-11-30. f-Oscillators and Nonlinear Coherent States. https://doi.org/10.1088/0031-8949%2F55%2F5%2F004

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