Explicit formulae for the eigenfunctions of theN-body Calogero model

2005/11/10 by Martin Hallnäs, Edwin Langmann · 8 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Cold Atom Physics and Bose-Einstein Condensates #Coupling (piping) #Eigenfunction #Eigenvalues and eigenvectors #Geometry #Harmonic oscillator #Inverse #Mathematical analysis #Mathematical physics #Mathematics #Nonlinear Waves and Solitons #Physics #Pure mathematics #Quantum #Quantum mechanics #Square (algebra) #Square root #math-ph #math.MP #msc:33 #msc:81U15 #nlin.SI

paper · pdf · doi:10.1088/0305-4470/39/14/002

published in Journal of Physics A Mathematical and General 39(14), 3511-3533 (Institute of Physics)

arxiv created 2005/11/10 · openalex publication_date 2006/03/22 · arxiv updated 2014/11/18 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/06

Abstract

We consider the quantum Calogero model, which describes N non-distinguishable quantum particles on the real line confined by a harmonic oscillator potential and interacting via two-body interactions proportional to the inverse square of the inter-particle distance. We elaborate a novel solution algorithm which allows us to obtain fully explicit formulae for its eigenfunctions, arbitrary coupling parameter and particle number. We also show that our method applies, with minor changes, to all Calogero models associated with classical root systems.

Citations

• Explicit Solution to the N-Body Calogero Problem
• Solution of the One-Dimensional N-Body Problems with Quadratic and/or Inversely Quadratic Pair Potentials
• A multispecies Calogero model

Cited by

• Singular Eigenfunctions of Calogero-Sutherland Type Systems and How to Transform Them into Regular Ones
• An Explicit Formula for Symmetric Polynomials Related to the Eigenfunctions of Calogero-Sutherland Models