ON ALGEBRAIC CLASSIFICATION OF QUASI-EXACTLY SOLVABLE MATRIX MODELS

Authors
Citation
Rz. Zhdanov, ON ALGEBRAIC CLASSIFICATION OF QUASI-EXACTLY SOLVABLE MATRIX MODELS, Journal of physics. A, mathematical and general, 30(24), 1997, pp. 8761-8770
Citations number
21
Categorie Soggetti
Physics,"Physycs, Mathematical
ISSN journal
03054470
Volume
30
Issue
24
Year of publication
1997
Pages
8761 - 8770
Database
ISI
SICI code
0305-4470(1997)30:24<8761:OACOQS>2.0.ZU;2-U
Abstract
We suggest a generalization of the Lie algebraic approach for construc ting quasi-exactly solvable one-dimensional Schrodinger equations. Thi s generalization is based on representations of Lie algebras by first- order matrix differential operators. We have classified inequivalent r epresentations of the Lie algebras of dimensions up to three by first- order matrix differential operators in one variable. Next we describe invariant finite-dimensional subspaces of the representation spaces of the one-, two-dimensional Lie algebras and of the algebra sl(2, R). T hese results enable us to construct multiparameter families of first-a nd second-order quasi-exactly solvable models. in particular, we have obtained two classes of quasi-exactly solvable matrix Schrodinger equa tions.