Momentum and Position Representations for the q-deformed Euclidean Quantum Space

2019/10/05 by Hartmut Wachter, Wachter, Hartmut
Mathematics · Physics and Astronomy · #16T05 (Primary) #81R50 (Secondary) #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #FOS: Physical sciences #Mathematical Physics (math-ph) #Noncommutative and Quantum Gravity Theories #Quantum Physics (quant-ph)

paper · pdf · doi:10.48550/arxiv.1910.02283

openalex publication_date 2019/10/05 · openalex created_date 2019/10/10 · openalex updated_date 2026/07/28

Abstract

We summarize some basics about mathematical tools of analysis for the q-deformed Euclidean space. We use the new tools to examine q-deformed eigenfunctions of the momentum or position operator within the framework of the star product formalism. We show that these two systems of functions are complete and orthonormal. With the q-deformed momentum or position eigenfunctions, we calculate matrix elements of the momentum or position operator. Considerations about expectation values and probability densities conclude the studies.

Citations

• Quantum mechanics as a statistical theory
• q-Difference Equations

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