Inequivalent quantizations of the rational Calogero model with a Coulomb type interaction

2008/05/31 by B. Basu-Mallick, Kumar S. Gupta, S. Meljanac +1 · 4 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Coulomb #Coupling (piping) #Nonlinear Waves and Solitons #Quantum Mechanics and Non-Hermitian Physics #Range (aeronautics) #Scattering #State (computer science) #Type (biology) #hep-th #math-ph #math.MP #nlin.SI

paper · pdf · doi:10.1140/epjc/s10052-008-0729-9

published in The European Physical Journal C 58(1), 159-170 (Springer Science+Business Media) · 15 pages, 3 figures, revtex4, typos corrected, to appear in EPJC

arxiv created 2008/08/22 · openalex publication_date 2008/09/23 · arxiv updated 2010/05/12 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

We consider the inequivalent quantizations of a N-body rational Calogero model with a Coulomb type interaction. It is shown that for certain range of the coupling constants, this system admits a one-parameter family of self-adjoint extensions. We analyze both the bound and scattering state sectors and find novel solutions of this model. We also find the ladder operators for this system, with which the previously known solutions can be constructed.

Citations

• Novel quantum states of the rational Calogero models without the confining interaction
• Exchange operator formalism for integrable systems of particles
• Equivalence of the Calogero-Sutherland model to free harmonic oscillators
• Pole structure of the Hamiltonian ζ-function for a singular potential
• Global properties of the spectrum of the Haldane-Shastry spin chain
• Explicit Solution to the N-Body Calogero Problem
• UNIVERSAL CORRELATIONS IN RANDOM MATRICES: QUANTUM CHAOS, THE 1/r2 INTEGRABLE MODEL, AND QUANTUM GRAVITY
• Inequivalent quantizations of the N=3 Calogero model with scale and mirror-S3 symmetry
• Origin of the anomalies: The modified Heisenberg equation
• Solution of the One-Dimensional N-Body Problems with Quadratic and/or Inversely Quadratic Pair Potentials
• Exact solution for the distribution of transmission eigenvalues in a disordered wire and comparison with random-matrix theory
• Bound states in one-dimensional quantum N-body systems with inverse square interaction
• A multispecies Calogero model