Feasibility and method of multi-step Hermitization of crypto-Hermitian quantum Hamiltonians

0556198 - ÚJF 2023 RIV DE eng J - Článek v odborném periodiku
Znojil, Miloslav
Feasibility and method of multi-step Hermitization of crypto-Hermitian quantum Hamiltonians.
European Physical Journal Plus. Roč. 137, č. 3 (2022), č. článku 335. ISSN 2190-5444. E-ISSN 2190-5444
Institucionální podpora: RVO:61389005
Klíčová slova: operators * symmetry
Obor OECD: Atomic, molecular and chemical physics (physics of atoms and molecules including collision, interaction with radiation, magnetic resonances, Mössbauer effect)
Impakt faktor: 3.4, rok: 2022
Způsob publikování: Omezený přístup
https://doi.org/10.1140/epjp/s13360-022-02567-0

Even the most economical conventional formulation of quantum mechanics called Schrodinger picture (SP) need not be always computationally or conceptually optimal. A Dyson-inspired remedy can sometimes be sought in a transfer of the calculations from the conventional and correct SP Hilbert space H into a 'false but friendlier' Hilbert space R. The difference (i.e., non-equivalence) between R. and H is given by a judicious simplification of the inner product. Although the Hamiltonian H itself appears non-Hermitian in R, its necessary Hermitization (mediated by a return to H) is usually feasible. If not, another eligible remedy is described in the present paper. Our basic idea lies in the introduction of a 'chained' auxiliary manipulation multiplet of inner-product spaces R-1, R-2, ..., R-N. At arbitrary N, the structure and properties of the resulting generalized SP (GSP) formulation of quantum mechanics of unitary systems (characterized by 'hiddenly Hermitian' observables) are described and discussed in detail. Nontrivial nature of the related multi-step Dyson-map composition laws and correspondences to the conventional Hermitian models are also revealed and clarified.
Trvalý link: http://hdl.handle.net/11104/0330490