A QUASI-EXACTLY SOLVABLE N-BODY PROBLEM WITH THE sl(N+1) ALGEBRAIC STRUCTURE

DOI10.1142/S0217751X99001457zbMath0967.81011arXivhep-th/9812157MaRDI QIDQ4949024

Xinrui Hou, Mikhail A. Shifman

Publication date: 27 April 2000

Published in: International Journal of Modern Physics A (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/hep-th/9812157

zbMATH Keywords

Calogero modelenergy-reflection symmetrycohomology parametermultiplicity of statesquadratic combination of the generators of \(\text{sl}(N+1)\)

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Many-body theory; quantum Hall effect (81V70) Groups and algebras in quantum theory and relations with integrable systems (81R12) Operator algebra methods applied to problems in quantum theory (81R15)

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Cites Work

• Lie algebras of differential operators and Lie-algebraic potentials
• Quantal problems with partial algebraization of the spectrum
• Quasi-exactly-solvable problems and sl(2) algebra
• QUASI-EXACTLY SOLVABLE MULTI-DIMENSIONAL SCHRÖDINGER EQUATIONS
• EXACT SOLVABILITY OF THE CALOGERO AND SUTHERLAND MODELS
• QUASI-EXACTLY-SOLVABLE MANY-BODY PROBLEMS
• Hidden algebras of the (super) Calogero and Sutherland models