在均匀强磁场中氢原子塞曼效应久期方程的简化公式

在均匀强磁场中,当氢原子的哈密顿量中B2项不能忽略时,氢原子的库仑场对称性遭到破坏,能级简并被全部解除.在应用变分法和数值法计算氢原子的能级过程中,计算十分复杂,而应用微扰法求解氢原子的能级,存在解久期方程的n2高阶行列式的困难.本文应用简并态微扰理论和球谐函数的性质,得到久期方程中非零微扰矩阵元普遍表达式.根据非零微扰矩阵元普遍表达式的性质,可以将氢原子塞曼效应久期方程的n2高阶行列式分解成1阶到n阶共n个低阶行列式的乘积,得到氢原子塞曼效应久期方程的简化公式,使得求解均匀强磁场中氢原子塞曼效应能级过程简化.而且由该公式可以得到氢原子在低能态时塞曼效应能级的解析解.根据该久期方程的简化公式计算了n=3氢原子塞曼效应一级近似能级.

Simplified formula of secular equation for hydrogen atom zeeman effect in a high magnetic field

The hydrogen atom's degenerates of energy levels are all relieved and its symmetry of coulomb field is destroyed in uniformity high magnetic field if the B~2 item in Hamilton quantum can't be ignored.The calculating of hydrogen atom's energy is very complicated in applying variational method and value method.It is difficult to calculate secular equation's n~2 high rank determinant by using the perturbation theory in degenerate state.The prevalent formula for nonzero perturbation matrix in the secular equation is gained by the perturbation theory in degenerate state and property of spherical harmonics function.According to the property of nonzero perturbation matrix's prevalent formula,the n~2 high rank determinant in secular equation for hydrogen atom zeeman effect can be decomposed into the produce of 1 rank to n rank determinant,and a simplified formula of secular equation for hydrogen atom zeeman effect is gained,thus the calculating in hydrogen atom's energy levels of zeeman effect is simplified in uniformity high magnetic field.In accordance with this simplified formula of hydrogen atom's energy levels of zeeman effect in low energy levels,the analytic solution is gained and the hydrogen atom's energy levels of first-order in n=3 state is calculated.