Canonical Discretization. I. Discrete faces of (an)harmonic oscillator
High Energy Physics - Theory
2016-12-21 v1 High Energy Physics - Lattice
Mathematical Physics
math.MP
Quantum Physics
Abstract
A certain notion of canonical equivalence in quantum mechanics is proposed. It is used to relate quantal systems with discrete ones. Discrete systems canonically equivalent to the celebrated harmonic oscillator as well as the quartic and the quasi-exactly-solvable anharmonic oscillators are found. They can be viewed as a translation-covariant discretization of the (an)harmonic oscillator preserving isospectrality. The notion of the deformation of the canonical equivalence leading to a dilatation-covariant discretization preserving polynomiality of eigenfunctions is also presented.
Keywords
Cite
@article{arxiv.hep-th/0004175,
title = {Canonical Discretization. I. Discrete faces of (an)harmonic oscillator},
author = {Alexander Turbiner},
journal= {arXiv preprint arXiv:hep-th/0004175},
year = {2016}
}
Comments
29 pages, LaTeX