Zig-zag-matrix algebras and solvable quasi-Hermitian quantum models

0574841 - ÚJF 2024 RIV GB eng J - Journal Article
Znojil, Miloslav
Zig-zag-matrix algebras and solvable quasi-Hermitian quantum models.
Journal of Physics A-Mathematical and Theoretical. Roč. 56, č. 33 (2023), č. článku 335301. ISSN 1751-8113. E-ISSN 1751-8121
Institutional support: RVO:61389005
Keywords : non-Hermitian quantum mechanics of unitary systems * a zig-zag-matrix class of N-state solvable models * closed formulae for wave functions * closed formula for general physical inner-product metric
OECD category: Pure mathematics
Impact factor: 2.1, year: 2022
Method of publishing: Open access
https://doi.org/10.1088/1751-8121/ace8d5

In quantum mechanics of unitary systems using non-Hermitian (or, more precisely, Theta-quasi-Hermitian) Hamiltonians H such that H(SIC) Theta = Theta H, the exactly solvable M-level bound-state models with arbitrary M <=infinity are rare. A new class of such models is proposed here, therefore. Its exact algebraic solvability (involving not only the closed formulae for wave functions but also the explicit description of all of the eligible metrics Theta) was achieved due to an extremely sparse (viz., just (2M-1)- parametric) but still nontrivial 'zig-zag-matrix' choice of the form of H.
Permanent Link: https://hdl.handle.net/11104/0344776