# Generalized hermite polynomials obtained by embeddings of the q-Heisenberg algebra

Banach Center Publications (1997)

- Volume: 40, Issue: 1, page 403-413
- ISSN: 0137-6934

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topSeifert, Joachim. "Generalized hermite polynomials obtained by embeddings of the q-Heisenberg algebra." Banach Center Publications 40.1 (1997): 403-413. <http://eudml.org/doc/252243>.

@article{Seifert1997,

abstract = {Several ways to embed q-deformed versions of the Heisenberg algebra into the classical algebra itself are presented. By combination of those embeddings it becomes possible to transform between q-phase-space and q-oscillator realizations of the q-Heisenberg algebra. Using these embeddings the corresponding Schrödinger equation can be expressed by various difference equations. The solutions for two physically relevant cases are found and expressed as Stieltjes Wigert polynomials.},

author = {Seifert, Joachim},

journal = {Banach Center Publications},

keywords = {-phase-space; -oscillator realization; -Heisenberg algebra; Stieltjes Wigert polynomials; Schrödinger equation; difference equations},

language = {eng},

number = {1},

pages = {403-413},

title = {Generalized hermite polynomials obtained by embeddings of the q-Heisenberg algebra},

url = {http://eudml.org/doc/252243},

volume = {40},

year = {1997},

}

TY - JOUR

AU - Seifert, Joachim

TI - Generalized hermite polynomials obtained by embeddings of the q-Heisenberg algebra

JO - Banach Center Publications

PY - 1997

VL - 40

IS - 1

SP - 403

EP - 413

AB - Several ways to embed q-deformed versions of the Heisenberg algebra into the classical algebra itself are presented. By combination of those embeddings it becomes possible to transform between q-phase-space and q-oscillator realizations of the q-Heisenberg algebra. Using these embeddings the corresponding Schrödinger equation can be expressed by various difference equations. The solutions for two physically relevant cases are found and expressed as Stieltjes Wigert polynomials.

LA - eng

KW - -phase-space; -oscillator realization; -Heisenberg algebra; Stieltjes Wigert polynomials; Schrödinger equation; difference equations

UR - http://eudml.org/doc/252243

ER -

## References

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- [9] T. Curtwright, C. Zachos, Paradigms of Quantum Algebras, ANL-HEP-PR-90-61, (1990).
- [10] Gaetano Fiore, The $S{O}_{q}(N,\mathbb{R})$-Symmetric Harmonic Oscillator on the Quantum Euclidean Space ${\mathbb{R}}_{q}^{N}$ and It’s Hilbert Space Structure, International Journal of Modern Physics, Vol. 8, 26 (1993) 4679-4729. Zbl0985.81545
- [11] Joachim Seifert, Quantum Mechanical Representations of the Q-Oscillator, forthcoming publication.

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