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arXiv:1808.03547 · Physics Letters A

Quasi-exactly solvable quantum systems with explicitly time-dependent Hamiltonians

Andreas Fring, Thomas Frith

Published Oct 30, 2018• 15 citations
arXivHTMLPDF
DOI
10.1016/j.physleta.2018.10.043

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We study the time evolution of a class of exactly solvable time-dependent quantum systems with a time-dependent Hamiltonian given by a linear combination of SU(1,1) and SU(2) generators with the help of the invariant Hermitian operator. The exact common solutions of the Schrödinger equations for both the SU(1,1) and SU(2) systems are obtained in terms of eigenstates of the invariant operator. The adiabatic and non-adiabatic Berry phases are calculated with the exact solutions. Moreover, we derive an explicit time-evolution operator which is used to investigate the time-dependent two-photon squeezing states and SU(2) squeezing states. The squeezing properties of the time-dependent SU(1,1) coherent states are also discussed.
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