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arXiv · 2212.01671

Heisenberg dynamics for non self-adjoint Hamiltonians: symmetries and derivations

Fabio Bagarello
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Abstract

In some recent literature the role of non self-adjoint Hamiltonians, $H\neq H^\dagger$, is often considered in connection with gain-loss systems. The dynamics for these systems is, most of the times, given in terms of a Schr\"odinger equation. In this paper we rather focus on the Heisenberg-like picture of quantum mechanics, stressing the (few) similarities and the (many) differences with respected to the standard Heisenberg picture for systems driven by self-adjoint Hamiltonians. In particular, the role of the symmetries, *-derivations and integrals of motion is discussed.

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Fabio Bagarello. 2022-12-03. Heisenberg dynamics for non self-adjoint Hamiltonians: symmetries and derivations. https://doi.org/10.1007/s11040-022-09443-4

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