Harmonic oscillator assemblies in a magnetic field

I. M. Ternov, Vladislav G. Bagrov, V. N. Zadorozhnyi

Arno Holz, Ernest E. Bergmann

M. Sebawe Abdalla

Virulh Sa‐Yakanit, J. Poulter

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.

GAO-FENG WEI, Long Chao-Yun, Long Zheng-Wen +1 more

In this paper, the isotropic charged harmonic oscillator in uniform magnetic field is researched in the non-commutative phase space; the corresponding exact energy is obtained, and the analytic eigenfunction is presented in terms of the confluent hypergeometric function. It is shown that in the non-commutative space, the isotropic charged harmonic oscillator in uniform magnetic field has the similar behaviors to the Landau problem.