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arXiv · 1808.03547

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

Andreas Fring·Thomas Frith
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Abstract

For a large class of time-dependent non-Hermitain Hamiltonians expressed in terms linear and bilinear combinations of the generators for an Euclidean Lie-algebra respecting different types of PT-symmetries, we find explicit solutions to the time-dependent Dyson equation. A specific Hermitian model with explicit time-dependence is analyzed further and shown to be quasi-exactly solvable. Technically we constructed the Lewis-Riesenfeld invariants making useof the metric picture, which is an equivalent alternative to the Schr\"{o}dinger, Heisenberg and interaction picture containing the time-dependence in the metric operator that relates the time-dependent Hermitian Hamiltonian to a static non-Hermitian Hamiltonian.

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Andreas Fring, Thomas Frith. 2018-08-10. Quasi-exactly solvable quantum systems with explicitly time-dependent Hamiltonians. https://doi.org/10.1016/j.physleta.2018.10.043

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