This paper is made of two chapters:In the first chapter q-deformed harmonic oscillator is derived from one dimension harmonic oscillator, then, The quantum Heisenberg-Wel algebra are obtained.

Even and odd generalized qs-coherent states of non-harmonic oscillator and their quantum statistics properties;

Nonclassical properties of superposition of eigenstates of the higher powers of annihilation operator of a non-harmonic oscillator;

The solution of the energy of non-harmonic oscillator by coherent state;

The energy change principle of anharmonic vibrator with the aviation of outer force is discussed.

Generalized Klauder-Perelomov coherent state of the anharmonic oscillator and their properties;

In this paper, we calculate the energy eigenvalue of a class of anharmonic oscillators by means of the self-consistent approximation.

It is shown that the possible higher squeezing order of the superposition state β >+e i φ β e i δ > of the generalized coherent states of the q deformed non harmonic oscillator can be expressed as k ≠2π n/δ ,with n an integer and δ the phase difference between the two generalized coherent states.

Quantum statistic properties of the eigenstates of the annihilation operator b N - (N≥2) of an non harmonic oscillator are studied.

Generalized Coherent States of Non Harmonic Oscillator and Generalized Coherent States of two Dimensional Harmonic Oscillator are investigated.