# 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…

## References

SHOWING 1-4 OF 4 REFERENCES

### Lie algebras in Fock space

- Mathematics
- 1997

A catalogue of explicit realizations of representations of Lie (super) algebras and quantum algebras in Fock space is presented.

### Lie-algebraic discretization of differential equations

- Mathematics
- 1995

A certain representation for the Heisenberg algebra in finite difference operators is established. The Lie algebraic procedure of discretization of differential equations with isospectral property is…

### The Askey-scheme of hypergeometric orthogonal polynomials and its q-analogue Report Fac

- Mathematics
- 1996

A system for automatically reading symbols, preferably figures, which are hand-written on an information carrier in an arrangement of squares provided on the information carrier. The images of these…

### Lie algebras and linear operators with invariant subspace

- 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
- 1994