Different faces of harmonic oscillator
@article{Turbiner1999DifferentFO, title={Different faces of harmonic oscillator}, author={Alexander V. Turbiner}, journal={arXiv: Mathematical Physics}, year={1999} }
Harmonic oscillator in Fock space is defined. Isospectral as well as polynomiality-of-eigenfunctions preserving, translation-invariant discretization of the harmonic oscillator is presented. Dilatationinvariant and polynomiality-of-eigenfunctions preserving discretization is also given.
3 Citations
Umbral calculus, difference equations and the discrete Schrödinger equation
- Mathematics
- 2004
In this paper, we discuss umbral calculus as a method of systematically discretizing linear differential equations while preserving their point symmetries as well as generalized symmetries. The…
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