# A Potential-Based Quantization Procedure of the Damped Oscillator

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## Abstract

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## 1. Introduction

## 2. The Lagrangian and Hamiltonian of a Damped Harmonic Oscillator

## 3. The Devil Is in the Details

## 4. The Quantization Procedure

## 5. Solution of Damping Wave Equation

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Appendix A

## References

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**Figure 1.**The dissipation caused shape damping of the distribution $\rho (x,t)$ of the damped oscillator in one time period. The applied parameter set is $m=1$; $\hslash =1$; $\omega =1$, $\gamma =0.8$, $\lambda =0.01$. The time period is $T=2\pi /\omega $. The peak of the initial distribution is at ${y}_{0}=-1$.

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**MDPI and ACS Style**

Márkus, F.; Gambár, K.
A Potential-Based Quantization Procedure of the Damped Oscillator. *Quantum Rep.* **2022**, *4*, 390-400.
https://doi.org/10.3390/quantum4040028

**AMA Style**

Márkus F, Gambár K.
A Potential-Based Quantization Procedure of the Damped Oscillator. *Quantum Reports*. 2022; 4(4):390-400.
https://doi.org/10.3390/quantum4040028

**Chicago/Turabian Style**

Márkus, Ferenc, and Katalin Gambár.
2022. "A Potential-Based Quantization Procedure of the Damped Oscillator" *Quantum Reports* 4, no. 4: 390-400.
https://doi.org/10.3390/quantum4040028