The complete menu of eligible metrics for a family of toy Hamiltonians $H \neq H^\dagger$ with real spectra
| dc.creator | Znojil, Miloslav | |
| dc.date | 2008-06-26 | |
| dc.date | 2008-07-29 | |
| dc.date.accessioned | 2026-07-07T09:53:06Z | |
| dc.date.available | 2026-07-07T09:53:06Z | |
| dc.description | An elementary set of non-Hermitian $N$ by $N$ matrices $H^{(N)}(λ) \neq [ H^{(N)}(λ)]^\dagger$ with real spectra is considered, assuming that each of these matrices represents a selfadjoint quantum Hamiltonian in an {\it ad hoc} Hilbert space of states ${\cal H}^{(physical)}$. The problem of an explicit specification of all of these spaces (i.e., in essence, of all of the eligible {\it ad hoc} inner products and metric operators $Θ$) is addressed. The problem is shown exactly solvable and, for every size $N=2,4,...$ and parameter $λ\in (-1,1)$ in matrix $H^{(N)}(λ)$, the complete $N-$parametric set of metrics $Θ^{(N)}_{α_1,α_2,...,α_N}(λ)$ is recurrently defined by closed formula. | |
| dc.description | 28 pp., 2 figures, thoroughly rewritten | |
| dc.identifier | https://arxiv.org/abs/0806.4295 | |
| dc.identifier | http://arxiv.org/abs/0806.4295 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/165835 | |
| dc.subject | Mathematical Physics | |
| dc.subject | 46C15; 81Q10 | |
| dc.title | The complete menu of eligible metrics for a family of toy Hamiltonians $H \neq H^\dagger$ with real spectra | |
| dc.type | text |