$$\theta(\hat{x},\hat{p})$$ -deformation of the Harmonic Oscillator in a 2D-phase Space

DOI10.1007/978-3-0348-0645-9_3zbMath1307.81035arXiv1211.0308OpenAlexW65585054MaRDI QIDQ5498843

Ezinvi Baloïtcha, Mahouton Norbert Hounkonnou, Dine Ousmane Samary, Sama Arjika

Publication date: 11 February 2015

Published in: Geometric Methods in Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1211.0308

zbMATH Keywords

energy spectrumHermite polynomials\(q\)-deformationharmonic oscillatormatrix elements\(\mathrm{su}(2)\)-algebra

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Quantum groups and related algebraic methods applied to problems in quantum theory (81R50) Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Applications of Lie groups to the sciences; explicit representations (22E70) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Phase-space methods including Wigner distributions, etc. applied to problems in quantum mechanics (81S30)

Cites Work

• Lorentz-covariant deformed algebra with minimal length
• Deformation quantization in the teaching of quantum mechanics
• Unnamed Item

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