On S-matrix of Schrodinger Operators with Non-Symmetric Zero-Range Potentials

Abstract

Non-self-adjoint Schrodinger operators which correspond to non-symmetric zero-range potentials are investigated. We show that various properties of these operators (eigenvalues, exceptional points, spectral singularities and the property of similarity to a self-adjoint operator) are completely determined by poles of the corresponding S-matrix.

References in corpus (5)

• Making Sense of Non-Hermitian Hamiltonians
• The physics of exceptional points
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• Closed formula for the metric in the Hilbert space of a PT-symmetric model
• Delta-Function Potential with a Complex Coupling

Cited by in corpus (3)

• Dirac lattices, zero-range potentials and self adjoint extension
• Solvable quantum lattices with nonlocal non-Hermitian endpoint interactions
• Bound states emerging from below the continuum in a solvable PT-symmetric discrete Schroedinger equation