Exactly solvable potentials and quantum algebras
V Spiridonov - Physical Review Letters, 1992 - APS
Physical Review Letters, 1992•APS
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 su q (1, 1).
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 su q (1, 1).
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 su q (1, 1).
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