Quantum mechanical applications of the large N method

The large N method, where N is the number of spatial dimensions, is a powerful, new technique for analytically determining the eigenstates of the Schroedinger equation, even for potentials which are in no sense small and hence not treatable by standard perturbation theory. A somewhat modified, physically motivated approach, which yields shifted large N expansions, incorporates exactly known analytic results into large N expansions, greatly enhancing their accuracy, simplicity and range of applicability. The rate of convergence can be further improved by using supersymmetry transformations. A systematic large N approach to potential scattering problems has also been recently developed