Canonical Discretization. I. Discrete faces of (an)harmonic oscillator

Details Canonical Discretization. I. Discrete faces of (an)harmonic oscillator Canonical Discretization. I. Discrete faces of (an)harmonic oscillator

2000-04-25

arxiv.org/abs/hep-th/0004175v1

Int.J.Mod.Phys. A16 (2001) 1579-1604

Physics

High Energy Physics

High Energy Physics - Theory

29 pages, LaTeX

Scientific paper

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 $q-$deformation of the canonical equivalence leading to a dilatation-covariant discretization preserving polynomiality of eigenfunctions is also presented.

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