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

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Instituto Nacional de Astrofísica, Óptica y Electrónica, Calle Luis Enrique Erro No. 1, 72840 Sta. María Tonantzintla, Puebla, Mexico
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Instituto de Ciencias Físicas, Universidad Nacional Autónoma de México, Apartado Postal 48-3, 62251 Cuernavaca, Morelos, Mexico
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Departamento de Física, CBI, Universidad Autónoma Metropolitana Iztapalapa, Apartado Postal 55-534, 09340 México D.F., Mexico
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Author to whom correspondence should be addressed.
Quantum Reports 2019, 1(1), 82-90; https://doi.org/10.3390/quantum1010009
Received: 10 June 2019 / Revised: 10 July 2019 / Accepted: 17 July 2019 / Published: 22 July 2019
We show that by using the quantum orthogonal functions invariant, we found a solution to coupled time-dependent harmonic oscillators where all the time-dependent frequencies are arbitrary. This system may be found in many applications such as nonlinear and quantum physics, biophysics, molecular chemistry, and cosmology. We solve the time-dependent coupled harmonic oscillators by transforming the Hamiltonian of the interaction using a set of unitary operators. In passing, we show that N time-dependent and coupled oscillators have a generalized orthogonal functions invariant from which we can write a Ermakov–Lewis invariant. View Full-Text
Keywords: time-dependent coupled oscillators; invariants; harmonic oscillators time-dependent coupled oscillators; invariants; harmonic oscillators
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 Reports 2019, 1, 82-90.

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