Exactly Solvable Potentials and Quantum Algebras

Details Exactly Solvable Potentials and Quantum Algebras Exactly Solvable Potentials and Quantum Algebras

1991-12-30

arxiv.org/abs/hep-th/9112075v2

Phys.Rev.Lett.69:398-401,1992

Physics

High Energy Physics

High Energy Physics - Theory

8 pages, LATEX. Essentially improved version

Scientific paper

10.1103/PhysRevLett.69.398

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. General solution includes Shabat's infinite number soliton system and leads to raising and lowering operators satisfying $q$-deformed harmonic oscillator algebra. In the latter case 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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