Zig-zag-matrix algebras and solvable quasi-Hermitian quantum models
Quantum Physics
2023-07-31 v1 Mathematical Physics
math.MP
Abstract
It is well known that the unitary evolution of a closed level quantum system can be generated by a non-Hermitian Hamiltonian with real spectrum. Its Hermiticity can be restored via an amended inner-product metric . In Hermitian cases the evaluation of the spectrum (i.e., of the bound-state energies) is usually achieved by the diagonalization of the Hamiltonian. In the non-Hermitian (or, more precisely, in the quasi-Hermitian) quantum mechanics we conjecture that the role of the diagonalized-matrix solution of the quantum bound-state problem could be transferred to a maximally sparse ``zig-zag-matrix'' representation of the Hamiltonians.
Keywords
Cite
@article{arxiv.2307.03439,
title = {Zig-zag-matrix algebras and solvable quasi-Hermitian quantum models},
author = {Miloslav Znojil},
journal= {arXiv preprint arXiv:2307.03439},
year = {2023}
}