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

0581037 - ÚJF 2024 RIV GB eng C - Conference Paper (international conference)
Lechtenfeld, O. - Znojil, Miloslav
Quasi-hermitian quantum mechanics and a new class of user-friendly matrix hamiltonians.
Journal of Physics: Conference series. Vol. 2667. Bristol: IOP, 2023 - (Burdík, Č.; Hrivňák, J.; Navrátil, O.; Pošta, S.), č. článku 012036. ISSN 1742-6588.
[International Symposium on Quantum Theory and Symmetries (QTS12). Praha (CZ), 24.07.2023-28.07.2023]
Institutional support: RVO:61389005
Keywords : quantum mechanics * Quasi-hermitian
OECD category: Pure mathematics
https://doi.org/10.1088/1742-6596/2667/1/012036

In the conventional Schrödinger's formulation of quantum mechanics the unitary evolution of a state ψ is controlled, in Hilbert spaceL, by a Hamiltonian ɧ which must be self-adjoint. In the recent, 'quasi-Hermitian' reformulation of the theory one replaces ɧ by its isospectral but non-Hermitian avatar H = Ω−1 𝖍Ω 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.
Permanent Link: https://hdl.handle.net/11104/0349601