Is it possible to construct exactly solvable models?

Details Is it possible to construct exactly solvable models? Is it possible to construct exactly solvable models?

1998-09-21

arxiv.org/abs/hep-th/9809152v3

Lect.Notes Phys. 539 (2000) 118-140

Physics

High Energy Physics

High Energy Physics - Theory

22 pages, 2 eps figures, latex 2epsilon, usepackage epsfig

Scientific paper

We develop a constructive method to derive exactly solvable quantum mechanical models of rational (Calogero) and trigonometric (Sutherland) type. This method starts from a linear algebra problem: finding eigenvectors of triangular finite matrices. These eigenvectors are transcribed into eigenfunctions of a selfadjoint Schr\"odinger operator. We prove the feasibility of our method by constructing a new "$AG_3$ model" of trigonometric type (the rational case was known before from Wolfes 1975). Applying a Coxeter group analysis we prove its equivalence with the $B_3$ model. In order to better understand features of our construction we exhibit the $F_4$ rational model with our method.

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