# Coherent States of Harmonic and Reversed Harmonic Oscillator

## Abstract

**:**

## 1. Introduction

## 2. Introducing a Trial Wave Function

## 3. Standard (Type-I) Coherent States of the HO

## 4. Type-II Solutions of the Harmonic Oscillator

#### 4.1. Completeness of Type-II States

#### 4.2. Mean Values and Uncertainty Product

## 5. Wave Packet Solutions for the RO

#### 5.1. Coherent States of the RO

#### 5.2. Mean Values

## 6. Application to the Kepler-Coulomb Problem

## 7. Conclusions

## Acknowledgments

## Conflicts of Interest

## Appendix A. Probability Density for Type-II States

## Appendix B. Proof of Completeness

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Rauh, A. Coherent States of Harmonic and Reversed Harmonic Oscillator. *Symmetry* **2016**, *8*, 46.
https://doi.org/10.3390/sym8060046

**AMA Style**

Rauh A. Coherent States of Harmonic and Reversed Harmonic Oscillator. *Symmetry*. 2016; 8(6):46.
https://doi.org/10.3390/sym8060046

**Chicago/Turabian Style**

Rauh, Alexander. 2016. "Coherent States of Harmonic and Reversed Harmonic Oscillator" *Symmetry* 8, no. 6: 46.
https://doi.org/10.3390/sym8060046