A Number of Quasi-Exactly Solvable N-body Problems

Abstract

We present several examples of quasi-exactly solvable $N$-body problems in one, two and higher dimensions. We study various aspects of these problems in some detail. In particular, we show that in some of these examples the corresponding polynomials form an orthogonal set and many of their properties are similar to those of the Bender-Dunne polynomials. We also discuss QES problems where the polynomials do not form an orthogonal set.

17pages, Revtex, no figure

References in corpus (2)

• Anti-isospectral Transformations, Orthogonal Polynomials and Quasi-Exactly Solvable Problems
• Do Quasi-Exactly Solvable Systems Always Correspond to Orthogonal Polynomials?

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• On the quasi - exact solvability of a singular potential in D - dimensions; confined and unconfined