f-Oscillators and Nonlinear Coherent States
Vladimir I. Man’ko, Giuseppe Marmo, E. C. G. Sudarshan, F. Zaccaria · CERN Document Server (European Organization for Nuclear Research) · 1996
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.