Solution to the Time-Dependent Coupled Harmonic Oscillators Hamiltonian with Arbitrary Interactions
Alejandro R. Urzúa, I. Ramos-Prieto, M. Fernández‐Guasti, H. M. Moya-Cessa · Quantum Reports · 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.