# Comparison of Harmonic Oscillator Model in Classical and Quantum Theories of Light-Matter Interaction

^{*}

## Abstract

**:**

## 1. Introduction

_{a}≈ 5.14⋅10

^{9}V/cm). As a result, the effect of electromagnetic radiation with an amplitude less than the atomic one on atomic electrons is weak, and the HO model is applicable [7].

## 2. Classical Harmonic Oscillator

#### 2.1. Model of Harmonic Oscillator

#### 2.2. Interaction of Charged Oscillator with Electromagnetic Radiation

#### 2.3. Excitation Energy of Oscillator by Electromagnetic Pulse

## 3. Bohr Correspondence Principle and Its Generalization

#### 3.1. Original Version of Bohr Correspondence Principle

#### 3.2. Generalization of Bohr Correspondence Principle

## 4. Charged Quantum Oscillator in the Electromagnetic Field

#### 4.1. Schwinger Formula for Excitation of Quantum Oscillator between Stationary States

_{0}according to the definition

#### 4.2. Classical HO Is a Driver of Quantum One

#### 4.3. Average Number of Excited Quanta

#### 4.4. Saturation Effect upon Pulsed Excitation of a Quantum Oscillator

## 5. Other Correspondences between Quantum Descriptions of Light–Matter Interaction and Classical HO Model

#### 5.1. HO Limit of Bloch Equations

#### 5.2. Accounting for the Damping of HO in the Framework of the Classical and Quantum Approaches

_{0}is given by Equation (18).

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**MDPI and ACS Style**

Astapenko, V.; Bergaliyev, T.
Comparison of Harmonic Oscillator Model in Classical and Quantum Theories of Light-Matter Interaction. *Foundations* **2023**, *3*, 549-559.
https://doi.org/10.3390/foundations3030031

**AMA Style**

Astapenko V, Bergaliyev T.
Comparison of Harmonic Oscillator Model in Classical and Quantum Theories of Light-Matter Interaction. *Foundations*. 2023; 3(3):549-559.
https://doi.org/10.3390/foundations3030031

**Chicago/Turabian Style**

Astapenko, Valery, and Timur Bergaliyev.
2023. "Comparison of Harmonic Oscillator Model in Classical and Quantum Theories of Light-Matter Interaction" *Foundations* 3, no. 3: 549-559.
https://doi.org/10.3390/foundations3030031