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Zhur. Eksptl'. i Teoret. Fiz.

ON PERTURBATION THEORY FOR LARGE QUANTUM SYSTEMS

Yu.L. Mentkovskii

Published Aug 1, 1960• 0 citations
OpenAlex

Abstract

A new form of the Van Hove--Hugenholtz perturbation theory expansion is proposed. The series obtained differ from the more familiar ones by the simplicity of the energy-denominators, a fact which may be useful, for example, in calculating the excited states. The deduction of the indicated expansions is quite simple. (auth)

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A perturbation theory is described which leads to two alternative methods for calculating the eigenvalues and normalized eigenstates of a perturbed Hamiltonian, the results being given to all orders in the perturbation. The expansions obtained are formulated in terms of two sets of partial sums which have simple, easily characterized forms, and they combine some of the advantages of both the Rayleigh-Schr\"odinger and Brillouin-Wigner perturbation methods while avoiding some of the difficulties of each. In particular, one form of the perturbation expansions given here will in most cases of interest have a larger radius of convergence than the Rayleigh-Schr\"odinger series. As is usual for infinite-order treatments, the explicit form of the final result applies only to nondegenerate levels. However, some of the intermediate relations obtained in the derivation are of general validity. Since certain classes of unlinked diagrams appear in the expansions, the method described here is not suitable for application to systems containing a large number of particles.