Quasi Exactly Solvable Difference Equations
Exactly Solvable and Integrable Systems
2009-11-13 v2 High Energy Physics - Theory
Mathematical Physics
math.MP
Quantum Physics
Abstract
Several explicit examples of quasi exactly solvable `discrete' quantum mechanical Hamiltonians are derived by deforming the well-known exactly solvable Hamiltonians of one degree of freedom. These are difference analogues of the well-known quasi exactly solvable systems, the harmonic oscillator (with/without the centrifugal potential) deformed by a sextic potential and the 1/sin^2x potential deformed by a cos2x potential. They have a finite number of exactly calculable eigenvalues and eigenfunctions.
Keywords
Cite
@article{arxiv.0708.0702,
title = {Quasi Exactly Solvable Difference Equations},
author = {Ryu Sasaki},
journal= {arXiv preprint arXiv:0708.0702},
year = {2009}
}
Comments
LaTeX with amsfonts, no figure, 17 pages, a few typos corrected, a reference renewed, 3/2 pages comments on hermiticity added