1998/09/30 by Oliver Haschke, Werner Ruehl
Physics and Astronomy · #hep-th
published as Lect.Notes Phys. 539 (2000) 118-140 · 22 pages, 2 eps figures, latex 2epsilon, usepackage epsfig
arxiv created 1998/10/01 · arxiv updated 2009/11/30
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 "AG3 model" of trigonometric type (the rational case was known before from Wolfes 1975). Applying a Coxeter group analysis we prove its equivalence with the B3 model. In order to better understand features of our construction we exhibit the F4 rational model with our method.