Year: 2018
Type: article
Abstract: We consider one-dimensional Schrödinger equations with potential x2M(ix)ε, where M ≥ 1 is an integer and ε is real, under appropriate parity and time (PT)-symmetric boundary conditions. We prove the phenomenon which was discovered by Bender and Boettcher by numerical computation: as ε changes, the real spectrum suddenly becomes non-real in the sense that all but finitely many eigenvalues become non-real. We find the limit arguments of these non-real eigenvalues E as E → ∞.
Source: Journal of Mathematical Physics
DOI: 10.1063/1.5016390
Authors: Alexandre Eremenko, Andrei Gabrielov
Institution: Purdue University West Lafayette
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Award: G6270382194
OpenAlex ID: W2769820481