  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.
