New Algebraic Quantum Many-body Problems

Abstract

We develop a systematic procedure for constructing quantum many-body problems whose spectrum can be partially or totally computed by purely algebraic means. The exactly-solvable models include rational and hyperbolic potentials related to root systems, in some cases with an additional external field. The quasi-exactly solvable models can be considered as deformations of the previous ones which share their algebraic character.

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References in corpus (3)

• Hidden Algebras of the (super) Calogero and Sutherland models
• A Quasi-Exactly Solvable N-Body Problem with the sl(N+1) Algebraic Structure
• Generalized Calogero-Sutherland systems from many-matrix models

Cited by in corpus (11)

• The Darboux transformation and algebraic deformations of shape-invariant potentials
• New spin Calogero-Sutherland models related to B_N-type Dunkl operators
• Exact solutions of an elliptic Calogero--Sutherland model
• A unified construction of generalised classical polynomials associated with operators of Calogero-Sutherland type
• Quasi-exact solvability beyond the SL(2) algebraization
• sl(M+1) Construction of Quasi-solvable Quantum M-body Systems
• Multidimensional quasi-exactly solvable potentials with two known eigenstates
• Exchange operator formalism for N-body spin models with near-neighbors interactions
• A Family of Quasi-solvable Quantum Many-body 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