On the real spectra of the Calogero model with complex coupling

2003/10/31 by Pijush K. Ghosh, Kumar S. Gupta
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Nonlinear Waves and Solitons #Quantum Mechanics and Non-Hermitian Physics #cond-mat #hep-th #nlin.SI #quant-ph

paper · pdf · doi:10.1016/j.physleta.2004.01.020

published as Phys.Lett. A323 (2004) 29-33 · revtex4 8 pages, 2 figures

arxiv created 2004/01/13 · openalex publication_date 2004/01/22 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the eigenvalue problem of the rational Calogero model with the coupling of the inverse-square interaction as a complex number. We show that although this model is manifestly non-invariant under the combined parity and time-reversal symmetry \calPT, the eigenstates corresponding to the zero value of the generalized angular momentum have real energies.

Citations

• Solution of the One-Dimensional N-Body Problems with Quadratic and/or Inversely Quadratic Pair Potentials
• Pseudo-Hermiticity of Hamiltonians under imaginary shift of the coordinate: real spectrum of complex potentials