The Harmonic Oscillator and Fields

Xie Yu-peng

Linear harmonic oscillator takes an important role in quantum mechanics.Many systems can be taken approximately as of linear harmonic oscillator.Consequently,the study on linear harmonic oscillator is significant in many ways.Using methods of formula and perturbation,this paper finds out the energy eigenvalue of one-dimensional linear harmonic oscillator in weak electric field,and presents clearly two typical solutions for the energy level of one-dimensional linear harmonic oscillator in weak electric field.

Günter Ludyk

Zhao Su-qin

The article studies a simple method for any energy level of three dimensional harmonic oscillator in uniform magnetic field.According to the perturbation theory in degenerate state,wave function of three dimensional harmonic oscillator in the uniform magnetic field,and the popular formula of perturbation matrix elements of three dimensional harmonic oscillator in the uniform magnetic field,the energy levels of first-order for n = 5 are calculated.A formula of energy level for three dimensional harmonic oscillator in the uniform magnetic field is given.

T. Banks

Stephen P. Martin

Bai Xian

The energy level structure and eigen wave functions of the q deformed harmonic oscillator in electric field are obtained by using the q differential.Glauber coherent states are constructed and its quantum properties are studied.It is shown that the dynamic actions are different from that of usual harmonic oscillator due to the deformation parameter′s influence.When q=1,q deformed harmonic oscillator degrades to usual harmonic oscillator.