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

• URL: http://arxiv.org/abs/2212.01671v1
• Date: Sat, 3 Dec 2022 18:56:02 GMT
• Title: Heisenberg dynamics for non self-adjoint Hamiltonians: symmetries and derivations
• Authors: Fabio Bagarello
• Abstract summary: We focus on the Heisenberg-like picture of quantum mechanics. In particular, the role of the symmetries, *-derivations and integrals of motion is discussed.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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