English

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

R2 v1 2026-06-21T09:05:01.170Z