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June 18, 2024
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December 5, 2024
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Abstract

Abstract


 


This article dis cusses the often-overlooked "damped" quantum harmonic oscillator, a vibrating system that loses energy over time. We bridge the classical-quantum divide, starting with the familiar equation of motion for a damped oscillator using Hooke's law. Delving into quantum mechanics, we explore how the Schrödinger equation governs its behavior. We then chart a path to understanding its energy changes and time evolution using mathematical tools like annihilation and creation operators, eigenstates, and eigenvalues. We then step through the understanding of its energy changes and time evolution using mathematical tools like annihilation and creation operators, eigenstates, and eigenvalues. Finally, we introduce the time-dependent Schrödinger equation for a damped quantum harmonic oscillator, which paves the way for stable oscillations


 


Keywords: Damped Quantum Oscillator; Canonical Quantization; Invariant Operator; Time-Dependent Schrödinger Equation


 


Abstrak


 


Artikel ini membahas osilator harmonik kuantum teredam, sebuah sistem getaran yang kehilangan energi seiring waktu, yang sering kali diabaikan dalam kajian fisika. Kami menjembatani kesenjangan antara mekanika klasik dan kuantum, dimulai dengan persamaan gerak osilator teredam berdasarkan hukum Hooke. Dalam ranah mekanika kuantum, kami mengeksplorasi bagaimana persamaan Schrödinger mengatur perilaku sistem ini. Selanjutnya, kami menelusuri perubahan energi dan evolusi waktu osilator ini menggunakan alat matematika seperti operator annihilasi dan kreasi, eigenstate, dan eigenvalue. Terakhir, kami memperkenalkan persamaan Schrödinger bergantung waktu untuk osilator harmonik kuantum teredam, yang membuka wawasan terhadap osilasi stabil dalam sistem ini.


 


Kata kunci: Osilator Kuantum Teredam; Kuantisasi Kanonik; Operator Invarian; Persamaan Schrödinger Bergantung Waktu

Keywords

Damped Quantum Oscillator Canonical Quantization Invariant Operator Time-Dependent Schrödinger Equation

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Copyright (c) 2024 Yahya Efendi, Faza Atika Anumillah, Muhammad Nurhuda

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How to Cite
Efendi, Y., Anumillah, F. A., & Nurhuda, M. (2024). Unveiling the Damped Quantum Harmonic Oscillator. Jurnal Kumparan Fisika, 7(3), 114–126. https://doi.org/10.33369/jkf.7.3.114-126
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References

  1. Valdez CRJ, Hernandez HHH, Acosta GC. Effective Description of the Quantum Damped Harmonic Oscillator: Revisiting the Bateman Dual System. arXiv preprint arXiv …. 2023;
  2. Dekker H. Classical and quantum mechanics of the damped harmonic oscillator. Physics Reports. 1981;80(1):1–110.
  3. Goudsmit SA. Quantum mechanics. Vol. 207, Journal of the Franklin Institute. Franklin Institute; 1929. 523–524 p.
  4. Sakurai JJ, Liboff RL. Modern Quantum Mechanics . Vol. 54, American Journal of Physics. Cambridge University Press; 1986. 668–668 p.
  5. Um CI, Yeon KH, George TF. The quantum damped harmonic oscillator. Physics Report. 2002;362(2–3):63–192.
  6. Chruściński D. Quantum mechanics of damped systems. II. Damping and parabolic potential barrier. Journal of Mathematical Physics. 2004;45(3):841–54.
  7. Chruściński D. Quantum damped oscillator II: Bateman’s Hamiltonian vs. 2D parabolic potential barrier. Annals of Physics. 2006;321(4):840–53.
  8. Bagarello F, Gargano F, Roccati F. Some remarks on few recent results on the damped quantum harmonic oscillator. Annals of Physics. 2020;414.
  9. Procurato JDL, Baybayon RN. Quantum Description of a Damped Coupled Harmonic Oscillator via White-Noise Analysis. CMU Journal of Science. 2020;
  10. Chruściński D. Quantum mechanics of damped systems. Journal of Mathematical Physics. 2003;44(9):3718–33.
  11. Kheirandish F. Quantum dynamics of a driven damped harmonic oscillator in Heisenberg picture: exact results and possible generalizations. European Physical Journal Plus. 2020;135(2).
  12. Bagarello F, Gargano F, Roccati F. A no-go result for the quantum damped harmonic oscillator. Physics Letters, Section A: General, Atomic and Solid State Physics. 2019;383(24):2836–8.
  13. Deniz C. Quantum Harmonic Oscillator. Oscillators - Recent Developments. 2019;841:12034.
  14. Breuer HP, Petruccione F. The Theory of Open Quantum Systems. Vol. 9780199213900, The Theory of Open Quantum Systems. Oxford University Press; 2007. 1–656 p.
  15. Gao Y, O’Connell RF, Tang Q Bin, Wang RM. The initial condition problem of damped quantum harmonic oscillator. European Physical Journal D. 2015;69(1).
  16. Korsch HJ. Lindblad dynamics of the damped and forced quantum harmonic oscillator: General solution. arXiv preprint arXiv:190801187. 2019;
  17. Pelap FB, Fomethe A, Fotue AJ, Tabue MPD. Time Dependent Entropy and Decoherence in a Modified Quantum Damped Harmonic Oscillator. Journal of Quantum Information Science. 2014;04(04):214–26.
  18. Guerrero J, López-Ruiz FF, Aldaya V, Cossío F. Symmetries of the quantum damped harmonic oscillator. Journal of Physics A: Mathematical and Theoretical. 2012;45(47).
  19. Bagarello F, Gargano F, Roccati F. A no-go result for the quantum damped harmonic oscillator. Physics Letters, Section A: General, Atomic and Solid State Physics. 2019;383(24):2836–8.
  20. Daeimohammad M. Influence of the counter-rotating terms on the quantum dynamics of the damped harmonic oscillator in a deformed bath. International Journal of Modern Physics B. 2019;33(13).
  21. Philbin TG. Quantum dynamics of the damped harmonic oscillator. New Journal of Physics. 2012;14.