Zig-zag-matrix algebras and solvable quasi-Hermitian quantum models
- URL: http://arxiv.org/abs/2307.03439v1
- Date: Fri, 7 Jul 2023 07:51:47 GMT
- Title: Zig-zag-matrix algebras and solvable quasi-Hermitian quantum models
- Authors: Miloslav Znojil
- Abstract summary: 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.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: It is well known that the unitary evolution of a closed $M-$level quantum
system can be generated by a non-Hermitian Hamiltonian $H$ with real spectrum.
Its Hermiticity can be restored via an amended inner-product metric $\Theta$.
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 $\Theta-$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.
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