Different faces of harmonic oscillator

  title={Different faces of harmonic oscillator},
  author={Alexander V. Turbiner},
  journal={arXiv: Mathematical Physics},
  • A. Turbiner
  • Published 9 May 1999
  • Computer Science
  • arXiv: Mathematical Physics
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. 

Umbral calculus, difference equations and the discrete Schrödinger equation

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  • Lie algebras, cohomologies and new findings in quantum mechanics (N. Kamran and P. J. Olver, eds.), AMS, vol. 160, pp. 263–310, 1994; “Lie-algebras and Quasi-exactly-solvable Differential Equations”, in CRC Handbook of Lie Group Analysis of Differential Equations, Vol.3: New Trends in Theoretical De
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