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Pramana

Generalized approach to applications of quantum time-dependent harmonic oscillator model with variable mass and frequency via dynamical invariant formalism

Metin Aktaş, Biswanath Rath, R. Sever

Published Jul 6, 2026• 0 citations
Publisher
DOI
10.1007/s12043-026-03155-y

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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.