# Solution to the Time-Dependent Coupled Harmonic Oscillators Hamiltonian with Arbitrary Interactions

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## Abstract

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## 1. Introduction

## 2. Ermakov–Lewis Invariant for $\mathit{N}$ Coupled Time-Dependent Harmonic Oscillators

#### The Classical Invariant

## 3. Two Coupled Time-Dependent Harmonic Oscillators

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**MDPI and ACS Style**

Urzúa, A.R.; Ramos-Prieto, I.; Fernández-Guasti, M.; Moya-Cessa, H.M.
Solution to the Time-Dependent Coupled Harmonic Oscillators Hamiltonian with Arbitrary Interactions. *Quantum Rep.* **2019**, *1*, 82-90.
https://doi.org/10.3390/quantum1010009

**AMA Style**

Urzúa AR, Ramos-Prieto I, Fernández-Guasti M, Moya-Cessa HM.
Solution to the Time-Dependent Coupled Harmonic Oscillators Hamiltonian with Arbitrary Interactions. *Quantum Reports*. 2019; 1(1):82-90.
https://doi.org/10.3390/quantum1010009

**Chicago/Turabian Style**

Urzúa, Alejandro R., Irán Ramos-Prieto, Manuel Fernández-Guasti, and Héctor M. Moya-Cessa.
2019. "Solution to the Time-Dependent Coupled Harmonic Oscillators Hamiltonian with Arbitrary Interactions" *Quantum Reports* 1, no. 1: 82-90.
https://doi.org/10.3390/quantum1010009