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arXiv · hep-th/9809152

Is it possible to construct exactly solvable models?

Oliver Haschke·Werner Ruehl
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Abstract

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 Schrödinger 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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Oliver Haschke, Werner Ruehl. 1998-10-01. Is it possible to construct exactly solvable models?. https://arxiv.org/abs/hep-th/9809152

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