Exactly Solvable Potentials and Quantum Algebras
High Energy Physics - Theory
2009-01-23 v2
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. General solution includes Shabat's infinite number soliton system and leads to raising and lowering operators satisfying -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 .
Cite
@article{arxiv.hep-th/9112075,
title = {Exactly Solvable Potentials and Quantum Algebras},
author = {V. Spiridonov},
journal= {arXiv preprint arXiv:hep-th/9112075},
year = {2009}
}
Comments
8 pages, LATEX. Essentially improved version