On Perturbation and Variation Methods
R E B Makinson, J. S. Turner
It is pointed out that the notation of the theory of functionals and the theorem in it analogous to Taylor's theorem facilitates a compact discussion of perturbation and variation methods in quantum mechanics, both for bound state and scattering problems. With this aid it is shown (i) how stationary expressions required for variation methods may be sought and found, (ii) that the perturbation and variation methods are virtually identical, (iii) that second order perturbations and expressions stationary to the second order may be found similarly, though these are complicated. The form found for the second order perturbation of bound states differs from that commonly used in that it does not explicitly involve the eigenfunctions of states other than that perturbed.
Proceedings of the Physical Society Section A•Oct 1, 1953•12 citations