Large-N expansions in quantum mechanics, atomic physics and some O(N) invariant systems

Abstract

Some selected topics on the subject of large-N expansions are reviewed here. A brief discussion of large-N critical phenomena is also presented. Generalizing the Schrödinger equation to N-dimensional space, the idea of the large-N limit is introduced in the context of quantum mechanic and the standard methods of 1/N expansion such as perturbed oscillator methods and Riccati equation methods are described in detail, with some interesting applications. Various other methods of 1/N expansion, namely the hypervirial 1/N expansion, the pseudospin formulation and the collective field method are also highlighted together with some of their important applications. Extension of the large-N scheme to the relativistic domain is presented and the application of the large-N concept to potential scattering is briefly discussed. © 1990.