2001/09/07 by B. Basu-Mallick, Kumar S. Gupta
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Cold Atom Physics and Bose-Einstein Condensates #hep-th #math-ph #math.MP #nlin.SI
paper · pdf · doi:10.1016/s0375-9601(01)00775-7
published as Phys.Lett.A292:36-42,2001 · 10 pages, Latex file, Minor typos corrected, Added one reference
arxiv created 2001/09/07 · openalex publication_date 2001/12/01 · arxiv updated 2011/07/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We investigate the existence of bound states in a one-dimensional quantum system of N identical particles interacting with each other through an inverse square potential. This system is equivalent to the Calogero model without the confining term. The effective Hamiltonian of this system in the radial direction admits a one-parameter family of self-adjoint extensions and the negative energy bound states occur when most general boundary conditions are considered. We find that these bound states exist only when N=3,4 and for certain values of the system parameters. The effective Hamiltonian for the system is related to the Virasoro algebra and the bound state wavefunctions exhibit a scaling behaviour in the limit of small inter-particle separation.