较强磁场中氢原子的能级(n=2～7)及其波函数

Energy Levels (n=2～7) and Wave Functions of Hydrogen Atom in Stronger Magnetic Field

基于简并微扰论和Mathematica软件平台,发展了一种简单可靠、全自动的计算方法研究磁场中的原子能级结构.考虑自旋磁矩和感生磁矩,计算了处在较强磁场中氢原子n=2~7的能级和波函数.讨论了简并微扰论的适用条件和能级分裂,绘制了概率角分布图和电子云图.数值结果表明：对于较强磁场,本方法是可靠和快捷的;一般情况下,磁场对能级的一级修正可以使简并完全解除（n=2~7）,但在一定条件下,会出现新的简并——偶然简并.

A simple and reliable method for investigating the behavior of atomic system in the magnetic field has been developed based on the perturbation theory and MATHEMATICA. Considering the spin magnetic moment and the induced magnetic moment, the energy levels （n =2~7） and wave functions of the hydrogen atom in the intermediate strong magnetic field were automatically calculated. The applicable condition of perturbation method and the energy level splitting are discussed. The probability angle distribution and the electron cloud are plotted. The numerical results show that for the intermediate strong magnetic field, the present method is reliable and fast. In general, the degeneracy of energy levels （n=2~7）can be completely removed; but under certain conditions, there is new degeneracy-accidental degeneracy.