Details
| Original language | English |
|---|---|
| Article number | 012036 |
| Number of pages | 8 |
| Journal | Journal of Physics: Conference Series |
| Volume | 2667 |
| Early online date | 18 Dec 2023 |
| Publication status | Published - 2023 |
| Event | 12th International Symposium on Quantum Theory and Symmetries, QTS 2023 - Prague, Czech Republic Duration: 24 Jul 2023 → 28 Jul 2023 |
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.
ASJC Scopus subject areas
- Physics and Astronomy(all)
- General Physics and Astronomy
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In: Journal of Physics: Conference Series, Vol. 2667, 012036, 2023.
Research output: Contribution to journal › Conference article › Research › peer review
}
TY - JOUR
T1 - Quasi-hermitian quantum mechanics and a new class of user-friendly matrix hamiltonians
AU - Lechtenfeld, Olaf
AU - Znojil, Miloslav
PY - 2023
Y1 - 2023
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85181076767&partnerID=8YFLogxK
U2 - 10.48550/arXiv.2308.15043
DO - 10.48550/arXiv.2308.15043
M3 - Conference article
AN - SCOPUS:85181076767
VL - 2667
JO - Journal of Physics: Conference Series
JF - Journal of Physics: Conference Series
SN - 1742-6588
M1 - 012036
T2 - 12th International Symposium on Quantum Theory and Symmetries, QTS 2023
Y2 - 24 July 2023 through 28 July 2023
ER -