Exactly solvable potentials and quantum algebras

1991/12/31 by V. P. Spiridonov, V. Spiridonov · 5 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Nonlinear Waves and Solitons #Quantum Mechanics and Non-Hermitian Physics #hep-th

paper · pdf · doi:10.1103/physrevlett.69.398

published as Phys.Rev.Lett.69:398-401,1992 · 8 pages, LATEX. Essentially improved version

openalex publication_date 1992/07/20 · arxiv created 1992/07/24 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A set of exactly solvable one-dimensional quantum-mechanical potentials is described. It is defined by a finite-difference-differential equation generating in the limiting cases the Rosen-Morse, harmonic, and P"oschl-Teller potentials. A general solution includes Shabat's infinite number soliton system and leads to raising and lowering operators satisfying a q-deformed harmonic-oscillator algebra. In the latter case the energy spectrum is purely exponential and physical states form a reducible representation of the quantum conformal algebra su_q(1,1).

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