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Generalized Gaudin models and Riccatians. (English) Zbl 0891.34082

Ławrynowicz, J. (ed.), Generalizations of complex analysis and their applications in physics. Warszawa: Polish Academy of Sciences, Inst. of Mathematics, Banach Cent. Publ. 37, 259-288 (1996).
The author outlines relations between Gaudin models and a hierarchy of Riccati-type operators, with fairly complicated expressions. Correspondences between these operators and Lie algebras of a given rank are also announced. Several possible generalizations and conjectures are mentioned. The reader is also referred to the author’s paper in [J. Part. Nucl. 20, 1185-1245 (1989)], and his recent book [Quasi-exactly solvable models in quantum mechanics, Bristol, Institute of Physics Publishing (1994; Zbl 0834.58042)] for a more detailed treatment of some of the issues.
For the entire collection see [Zbl 0856.00020].

MSC:

34L40 Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.)
81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
35P05 General topics in linear spectral theory for PDEs
17B66 Lie algebras of vector fields and related (super) algebras

Citations:

Zbl 0834.58042
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