A quasi-exactly solvable N-body problem with the sl(N + 1) algebraic structure

Xinrui Hou, M. Shifman

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Abstract

Starting from a one-particle quasi-exactly solvable system, which is characterized by an intrinsic sl(2) algebraic structure and the energy-reflection symmetry, we construct a daughter N-body Hamiltonian presenting a deformation of the Calogero model. The features of this Hamiltonian are (i) it reduces to a quadratic combination of the generators of Sl(N + 1); (ii) the interaction potential contains two-body terms and interaction with the force center at the origin; (iii) for quantized values of a certain cohomology parameter n it is quasi-exactly solvable, the multiplicity of states in the algebraic sector is (N+n)!(N!n!); (iv) the energy-reflection symmetry of the parent system is preserved.

Original languageEnglish (US)
Pages (from-to)2993-3003
Number of pages11
JournalInternational Journal of Modern Physics A
Volume14
Issue number19
DOIs
StatePublished - Jul 30 1999

Bibliographical note

Funding Information:
Useful discussions and correspondence with A. Turbiner and A. Ushveridze are gratefully acknowledged. This work was supported in part by DOE under the grant number DE-FG02-94ER40823.

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