简并基态最陡下降微扰理论

本文证明,Cioslowski所引入的一个全新的量子力学计算方案,非简并基态最陡下降微扰理论,通过按对称性选择合适的零级试探波函数后,可以处理简并基态的微扰分裂问题由于最陡下降微扰理论既避免了通常的其他微扰理论需要对各个基矢量无限求和的或求解一组微分方程的缺陷,又具有逐步迭代改善计算结果的优点,本文引进的计算方案可望在原子分子及其他多粒子体系能级的微扰分裂计算中得到广泛应用。 关键词：

DEGENERATE GROUND STATE STEEPEST DESCENT PERTURBATION THEORY

In this paper, an entire new approach for quantum mechanics calculation, the non-degenerate ground state steepest descent perturbation theory (SDPT) suggested by Cioslowski is developed and extended for dealing with degenerate ground state problem. Using sysmme-try adapted trial wave ket, the SDPT iteration for different sublevel is independent from each other and improves its eigen energy and wave function step by step. Therefore, the steepest descent perturbation theory can be used to calculate the low symmetry splitting of degenerate ground state and the correlation energy to arbitrary precison. Unlike other perturbation theory, this does not require either infinite summation overlstates or the solution of a set of differential equations, it could be expected wide adaptability in the calculation of energy level perturbation splitting of atoms, molecules and orther many body quantum system.