量子微扰论的Dalgarno-Lewis方法和应用

Dalgarno-Lewis approach of quantum perturbation and its application

Dalgarno-Lewis方法是获得微扰论中修正项的精确值的一种优美方法,避免了一般微扰论中各阶修正项公式中的无穷项的求和困难.本文在阐述了Dalgarno-Lewis方法,并用此法求解了弱电场作用下一维半无限空间中库仑势作用下的能级和波函数问题,给出了体系能量精确的三阶修正量和精确到一阶的波函数.所得结果简洁和具有规律性,显示了Dalgarno-Lewis方法的优点.

Dalgarno-Lewis approach is an elegant perturbation method which provides exact correction terms to a given order and it avoies the difficulties of summing up infinite terms in the ordinary perturbation approaches.We expound Dalgarno-Lewis method and apply it to the problems of energy levels and wave functions of an atom in a semi-space with a coulomb potential and an external weak electric field.The energy levels up to third order and wave functions to first order are calculated.The results are concise and regular in forms,which show the advantages of the Dalgarno-Lewis perturbation method.