Is it possible to construct exactly solvable models?
- 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 an " 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:||O. Haschke, W. Rühl|
|URN (permanent link):||urn:nbn:de:hbz:386-kluedo-11241|
|Language of publication:||English|
|Year of Completion:||1998|
|Year of Publication:||1998|
|Publishing Institute:||Technische Universität Kaiserslautern|
|Faculties / Organisational entities:||Fachbereich Physik|