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Quasi-hermitian quantum mechanics and a new class of user-friendly matrix hamiltonians

authored by
Olaf Lechtenfeld, Miloslav Znojil
Abstract

In the conventional Schrödinger's formulation of quantum mechanics the unitary evolution of a state ψ is controlled, in Hilbert space L, by a Hamiltonian h which must be self-adjoint. In the recent, "quasi-Hermitian"reformulation of the theory one replaces h by its isospectral but non-Hermitian avatar H = ω-1 o ω with ω†ω = Θ ≠ I. Although acting in another, manifestly unphysical Hilbert space H, the amended Hamiltonian H ≠ H † can be perceived as self-adjoint with respect to the amended inner-product metric Θ. In our paper motivated by a generic technical "user-unfriendliness"of the non-Hermiticity of H we introduce and describe a specific new family of Hamiltonians H for which the metrics Θ become available in closed form.

Organisation(s)
Institut für Theoretische Physik
Riemann Center for Geometry and Physics
External Organisation(s)
Czech Academy of Sciences
University of Hradec Kralove
Durban University of Technology
Type
Konferenzaufsatz in Fachzeitschrift
Journal
Journal of Physics: Conference Series
Volume
2667
No. of pages
8
ISSN
1742-6588
Publication date
2023
Publication status
Veröffentlicht
Peer reviewed
Yes
ASJC Scopus Sachgebiete
Physik und Astronomie (insg.)
Electronic version(s)
https://doi.org/10.48550/arXiv.2308.15043 (Access: Offen)
https://doi.org/10.1088/1742-6596/2667/1/012036 (Access: Offen)