Quantization of Dissipative Anisotropic Harmonic Oscillators

Authors

  • Bashar M. Al-khamiseh MEU Research Unit, Middle East University, Amman 11118, Jordan
  • Yazen M. Alawaideh MEU Research Unit, Middle East University, Amman 11118, Jordan
  • Dumitru Baleanu Department of Computer Science and Mathematics, Lebanese American University, Beirut,11 Lebanon
  • Hayat Issaadi USTHB University, Operational Research Department, BP 32 El-Alia,Bab-Ezzouar, 16111 Algeria
  • Muhammad Bilal Department of Physics, Shanghai University, Shanghai 200444, China
  • Shajar Abbas AS (Ayub Shah), Institute of Mathematics and Research Centre, Multan, Pakistan
  • Hala Ghannam Department of Basic Sciences, Middle East University, Amman 11831, Jordan

DOI:

https://doi.org/10.29020/nybg.ejpam.v18i2.5828

Keywords:

Poisson bracket, creation and annihilation operators, WKB approximation, staeckel boundary conditions, Two-Dimensional Anisotropic, Harmonic Oscillator dissipative.

Abstract

In this study, we developed a Hamiltonian framework for the anisotropic harmonic oscillator and applied the Hamilton-Jacobi equations, which are particularly well-suited for this approach. We were able to find the action function by including boundary conditions in the study of a dissipative anisotropic harmonic oscillator. To quantize the system, we employed three distinct methods: the WKB approximation, canonical quantization, and the creation and annihilation operator technique. The quantization of the Heisenberg equations was achieved by reformulating them using Poisson bracket quantum variables. Through the application of creation and annihilation operators, we derived the energy levels and quantum states of the system. The results demonstrated complete consistency across the different methods. This model exhibits strong agreement among the solutions derived from various approaches, highlighting its importance in advancing the understanding of dissipative quantum systems.

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Published

2025-05-01

Issue

Vol. 18 No. 2: (April 2025)

Section

Mathematical Physics

License

Copyright (c) 2025 Bashar M. Al-khamiseh, Yazen M. Alawaideh, Dumitru Baleanu, Hayat Issaadi, Muhammad Bilal, Shajar Abbas, Hala Ghannam

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How to Cite

Quantization of Dissipative Anisotropic Harmonic Oscillators. (2025). European Journal of Pure and Applied Mathematics, 18(2), 5828. https://doi.org/10.29020/nybg.ejpam.v18i2.5828