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arXiv:quant-ph/0205006 · Physics Letters B

Exact quantum-statistical dynamics of time-dependent generalized oscillators

Sang Pyo Kim, Don Nelson Page

Published May 7, 2013• 4 citations
arXivHTMLPDF
DOI
10.1016/j.physletb.2013.05.006

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By using the Lewis–Riesenfeld invariants theory, we investigate the quantum dynamics of a two-dimensional (2D) time-dependent coupled oscillator. We introduce a unitary transformation and show the conditions under which the invariant operator is uncoupled to describe two simple harmonic oscillators with time-independent frequencies and unit masses. The decouplement allows us to easily obtain the corresponding eigenstates. The generalization to three-dimensional (3D) time-dependent coupled oscillator is briefly discussed where a diagonalized invariant, which is exactly the sum of three simple harmonic oscillators, is obtained under specific conditions on the parameters.