求近似波函数的一种方法

设H为量子体系的哈密顿算符,以算符(λ-H)和(H-λ)^-1作用于近似波函数ψ_k⁽⁰⁾。我们证明了,如果作用得到的函数中φ_k在H的变量的整个区间是连续、有限和平方可积的,则它们是比ψ_k⁽⁰⁾更接近于本征态ψ_k的近似波函数。由φ_k计算H的平均值接近于以{ψ_k⁽⁰⁾}为无微扰态的二级微扰的计算值。用此法计算类氢离子的极化率,得到很好的结果。

A METHOD FOR OBTAINING APPROXIMATE WAVE FUNCTIONS

An approximate wave function ψ_k⁽⁰⁾ is operated on by the operators λ-H and (H-λ)^-1, where H is the Hamiltonian operator of the quantum system under consideration. We have shown that, if the resulting function φ_k is continuous, finite and square integrable in the whole domain of the variables of H, it is a better approximate wave function to the eigenstate ψ_k of the system than ψ_k⁽⁰⁾ is. The expecting value of H, calculated with φ_k as wave function approaches to that calculated by the method of second order perturbation with {ψ_k⁽⁰⁾} as unperturbated states. Polarizabilities of hydrogen-like ions are calculated and good results are obtained.