PT-symmetric eigenvalues for homogeneous potentials

PT-symmetric eigenvalues for homogeneous potentials

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 r...

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Veröffentlicht in:Journal of mathematical physics 2018-05, Vol.59 (5)
Hauptverfasser: Eremenko, Alexandre, Gabrielov, Andrei
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Sprache:eng
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Boundary conditions
Eigenvalues
Numerical analysis
Schrodinger equation
Symmetry
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description 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 → ∞.
doi_str_mv 10.1063/1.5016390
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subjects Boundary conditions
Eigenvalues
Numerical analysis
Schrodinger equation
Symmetry
title PT-symmetric eigenvalues for homogeneous potentials
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