Non-stationary quantum mechanics in hybrid non-Hermitian interaction representation

DOI10.1016/J.PHYSLETA.2023.128655arXiv2301.06128MaRDI QIDQ6423441

Publication date: 15 January 2023

Abstract: A reformulation of quantum mechanics called ``hybrid interaction picture (HIP) is proposed. In contrast to its current non-Hermitian-interaction-picture (NIP) predecessor the new formalism combines a simplification of the NIP Hilbert-space metric with an innovative preconditioning of the observables of interest. Via an illustrative example it is shown that the idea might open new ways towards optimal model-building strategies in quantum theory of unitary systems.

Mathematics Subject Classification ID

Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product) (46C05) Schrödinger operator, Schrödinger equation (35J10) Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems) (93C30) Nonselfadjoint operator theory in quantum theory including creation and destruction operators (81Q12) Time-dependent Schrödinger equations and Dirac equations (35Q41) Mathematical modeling or simulation for problems pertaining to quantum theory (81-10)

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