Quasi-Exactly-Solvable Many-Body Problems

Abstract

Explicit examples of quasi-exactly-solvable $N$-body problems on the line are presented. These are related to the hidden algebra $s{l}_N$, and they are of two types -- containing up to $N$ (infinitely-many eigenstates are known, but not all) and up to 6 body interactions only (a finite number of eigenstates is known). Both types degenerate to the Calogero model.

11 pages, LaTeX; a slight revision of statements made, one reference added, typos corrected; to appear in MPLA

Cited by in corpus (23)

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• Exact solutions of an elliptic Calogero--Sutherland model
• Solvability of the Hamiltonians related to exceptional root spaces: rational case
• A Quasi-Exactly Solvable N-Body Problem with the sl(N+1) Algebraic Structure
• New Algebraic Quantum Many-body Problems
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• sl(M+1) Construction of Quasi-solvable Quantum M-body Systems
• Exactly Solvable Three-body SUSY Systems with Internal Degrees of Freedom
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• Four-body problem in d-dimensional space: ground state, (quasi)-exact-solvability. IV
• Four-body (an)harmonic oscillator in $d$-dimensional space: $S$-states, (quasi)-exact-solvability, hidden algebra $sl(7)$
• Weak-QES extensions of the Calogero model
• From Quantum $A_N$ (Calogero) to $H_4$ (Rational) Model
• A Family of Quasi-solvable Quantum Many-body Systems
• Quasi exactly solvable matrix Schroedinger operators
• Additional restrictions on quasi-exactly solvable systems
• A Many-body Generalization of Quasi-solvable Models with Type C N-fold Supersymmetry (I) Regular Cases
• A New Construction of Quasi-solvable Quantum Many-body Systems of Deformed Calogero-Sutherland Type