1998/03/24 by Hideaki Ujino, Akinori Nishino, Miki Wadati · 11 citations
Mathematics · Physics and Astronomy · #Algebraic number #Algebraic structures and combinatorial models #Basis (linear algebra) #Boson #Compact operator #Creation and annihilation operators #Eigenfunction #Eigenvalues and eigenvectors #Fock space #Geometry #Hamiltonian (control theory) #Harmonic oscillator #Ladder operator #Mathematical analysis #Mathematical physics #Mathematics #Nonlinear Waves and Solitons #Operator (biology) #Orthogonal basis #Orthogonal polynomials #Physics #Polynomial #Pure mathematics #Quantum #Quantum Mechanics and Non-Hermitian Physics #Quantum mechanics #cond-mat.stat-mech #hep-th #nlin.SI #solv-int
paper · pdf · doi:10.1016/s0375-9601(98)00769-5
published in Physics Letters A 249(5-6), 459-464 (Elsevier BV) · 12pages, REVTeX
arxiv created 1998/03/24 · openalex publication_date 1998/12/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We demonstrate an algebraic construction of all the simultaneous eigenfunctions of the conserved operators for distinguishable particles governed by the Calogero Hamiltonian. Our construction is completely parallel to the construction of the Fock space for decoupled quantum harmonic oscillators. The simultaneous eigenfunction does not coincide with the non-symmetric Hi-Jack polynomial, which shows that the conserved operators derived from the number operators of the decoupled quantum harmonic oscillators are algebraically different from the known ones derived by the Dunkl operator formulation.