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q-quantum plane,ψ(q)-umbral calculus, and all that

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Czechoslovak Journal of Physics Aims and scope

Abstract

It is known that one can formulateq-extended finite operator calculus with help of “quantumq-plane”q-commuting variablesA, B : AB − qBA ≡ [A, B]q=0.

We shall recall this simple fact in its natural entourage which is the so-calledψ(q)-extension of Rota’s finite operator calculus. We aim to convince the audience that this is a natural and elementary method for formulation and treatment ofq-extended and possiblyR-extended orψ(q)-extended models for quantum-likeψ(q)-deformed oscillators.

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Authors and Affiliations

  1. Institute of Computer Science, Białystok University, ul.Sosnowa 64, PL-15-887, Białystok, Poland

    A. K. Kwaśniewski

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  1. A. K. Kwaśniewski
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Kwaśniewski, A.K. q-quantum plane,ψ(q)-umbral calculus, and all that. Czech J Phys 51, 1368–1373 (2001). https://doi.org/10.1023/A:1013334406596

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  • DOI: https://doi.org/10.1023/A:1013334406596

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