Is it possible to construct exactly solvable models?
- 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.
Author: | Oliver Haschke, Werner Rühl |
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URN: | urn:nbn:de:hbz:386-kluedo-10264 |
Document Type: | Preprint |
Language of publication: | English |
Year of Completion: | 1998 |
Year of first Publication: | 1998 |
Publishing Institution: | Technische Universität Kaiserslautern |
Date of the Publication (Server): | 2000/04/06 |
Faculties / Organisational entities: | Kaiserslautern - Fachbereich Physik |
DDC-Cassification: | 5 Naturwissenschaften und Mathematik / 530 Physik |
Licence (German): | Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011 |