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)