Exactly solvable potentials and quantum algebras
- 20 July 1992
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review Letters
- Vol. 69 (3), 398-401
- https://doi.org/10.1103/physrevlett.69.398
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. 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 (1,1).
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