Exact solutions of an elliptic Calogero--Sutherland model

Abstract

A model describing N particles on a line interacting pairwise via an elliptic function potential in the presence of an external field is partially solved in the quantum case in a totally algebraic way. As an example, the ground state and the lowest excitations are calculated explicitly for N=2.

4 pages, 3 figures, typeset with RevTeX 4b3 and AMS-LaTeX

References in corpus (7)

• Black Holes and Calogero Models
• Calogero-Moser Systems in SU(N) Seiberg-Witten Theory
• A Quasi-Exactly Solvable N-Body Problem with the sl(N+1) Algebraic Structure
• New Algebraic Quantum Many-body Problems
• On the explicit solutions of the elliptic Calogero system
• Non-Abelian Chern-Simons Particles in an External Magnetic Field
• Weak-QES extensions of the Calogero model

Cited by in corpus (19)

• One-Dimensional Quasi-Exactly Solvable Schrödinger Equations
• A_N-type Dunkl operators and new spin Calogero-Sutherland models
• Quasi-Exact Solvability and the direct approach to invariant subspaces
• Solvability of the Hamiltonians related to exceptional root spaces: rational case
• The Heun equation and the Calogero-Moser-Sutherland system II: perturbation and algebraic solution
• Explicit solution of the (quantum) elliptic Calogero-Sutherland model
• Quasi-exact solvability beyond the SL(2) algebraization
• Source identity and kernel functions for elliptic Calogero-Sutherland type systems
• sl(M+1) Construction of Quasi-solvable Quantum M-body Systems
• Three-body problem in $d$-dimensional space: ground state, (quasi)-exact-solvability
• Quasi-exact-solvability of the $A_2/G_2$ Elliptic model: algebraic forms, $sl(3)/g^{(2)}$ hidden algebra, polynomial eigenfunctions
• Source identity and kernel functions for Inozemtsev-type systems
• Inequivalent Quantizations of the N = 3 Calogero model with Scale and Mirror-S_3 Symmetry
• Exchange operator formalism for N-body spin models with near-neighbors interactions
• Multiple algebraisations of an elliptic Calogero-Sutherland model
• The $B{C}_1$ Elliptic model: algebraic forms, hidden algebra $sl(2)$, polynomial eigenfunctions
• A Family of Quasi-solvable Quantum Many-body Systems
• Quasi exactly solvable (QES) equations with multiple algebraisations
• Quasi-exact solvability of Inozemtsev models