Equivalence of the Calogero-Sutherland model to free harmonic oscillators

1997/10/31 by N. Gurappa, Prasanta K. Panigrahi, Prasanta. K. Panigrahi · 78 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Cold Atom Physics and Bose-Einstein Condensates #Eigenfunction #Eigenvalues and eigenvectors #Equivalence (formal languages) #Geometry #Harmonic oscillator #Inverse #Mathematical analysis #Mathematics #Matrix similarity #Nonlinear Waves and Solitons #Physics #Pure mathematics #Quantum mechanics #Transformation (genetics) #cond-mat #hep-th

paper · pdf · doi:10.1103/physrevb.59.r2490

published in Physical review. B, Condensed matter 59(4), R2490-R2493 (American Physical Society) · 9 pages, REVTeX, Completely revised, few new equations and references are added

arxiv created 1997/12/10 · openalex publication_date 1999/01/15 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

A similarity transformation is constructed, through which a system of particles interacting with inverse-square two-body and harmonic potentials in one dimension can be mapped identically to a set of free harmonic oscillators. This equivalence provides a straightforward method to find the complete set of eigenfunctions, the exact constants of motion, and a linear W_1+\ensuremath∞ algebra associated with this model. It is also demonstrated that a large class of models with long-range interactions, both in one and higher dimensions can be made equivalent to decoupled oscillators.

Citations

• Exchange operator formalism for integrable systems of particles
• Exact operator solution of the Calogero-Sutherland model
• Solution of the One-Dimensional N-Body Problems with Quadratic and/or Inversely Quadratic Pair Potentials
• Interacting Fermion Systems from Two Dimensional QCD
• Exact solutions of generalized Calogero-Sutherland models: BCN and CN cases

Cited by

• Hidden symmetries of integrable conformal mechanical systems
• Orthogonal basis for the energy eigenfunctions of the Chern-Simons matrix model
• New nonsymmetric orthogonal basis for the Calogero model with distinguishable particles
• The Calogero–Moser equation system and the ensemble average in the Gaussian ensembles
• Heisenberg symmetry and collective modes of one dimensional unitary correlated fermions
• Inequivalent quantizations of the rational Calogero model with a Coulomb type interaction
• Quantization and conformal properties of a generalized Calogero model