Exactly Solvable Potentials and Quantum Algebras

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 Pöschl-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 $s{u}_q(1,1)$.

8 pages, LATEX. Essentially improved version

References in corpus (1)

• Deformed Conformal and Supersymmetric Quantum Mechanics

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