德拜势中类氢原子能级近似解析式与幂级数求解

Solution of the level of approximation analytic formula and the solution of power series for hydrogen-like atoms in condition of Debye potential

对德拜势 (Debye)中类氢原子的能级问题采用Rayleigh Schr dinger微扰展开 ,给出了能级的一阶修正与原子能级的近似解析式。同时 ,采用波函数幂级数解法 ,求得了德拜势下相关的递推关系。在此基础上 ,利用能量自洽法 ,求出了相当于二阶修正的德拜势下类氢原子的能级值 ,并就其计算结果与数值解进行了比较。同时 ,讨论了相应的临界束缚能态与截断条件。

The first-order revision and the approximation analytical formula of the energy levels for hydrogen-like atoms in condition of the Debye shielding potential are achieved by means of the Rayleigh-Schrdinger perturbation theory, meanwhile, the corresponding recurrence relations are got with the use of the solution of power series. Basic on mentioned above and with the use of energy consistent method the equivalent value of second-order revision in condition of the Debye shielding potential as well be got and the result is compared with the data obtained by the numerical method. Beside, The cut of bond state and corresponding conditions are discussed.