Quasi-exactly solvable problems and random matrix theory

Abstract

There exists an exact relationship between the quasi-exactly solvable problems of quantum mechanics and models of square and rectangular random complex matrices. This relationship enables one to reduce the problem of constructing topological ($1/N$) expansions in random matrix models to the problem of constructing semiclassical expansions for observables in quasi-exactly solvable problems. Lie algebraic aspects of this relationship are also discussed.

nine pages in Latex, no figures

References in corpus (2)

• From polymers to quantum gravity: triple-scaling in rectangular matrix models
• Quartic Anharmonic Oscillator and Random Matrix Theory

Cited by in corpus (1)

• On time-dependent quasi-exactly solvable models