On elements of the Lax-Phillips scattering scheme for PT-symmetric operators

Abstract

Generalized PT-symmetric operators acting an a Hilbert space $\mathfrak{H}$ are defined and investigated. The case of PT-symmetric extensions of a symmetric operator $S$ is investigated in detail. The possible application of the Lax-Phillips scattering methods to the investigation of PT-symmetric operators is illustrated by considering the case of 0-perturbed operators.

References in corpus (3)

• Making Sense of Non-Hermitian Hamiltonians
• Scattering theory with localized non-Hermiticities
• PT Symmetric, Hermitian and P-Self-Adjoint Operators Related to Potentials in PT Quantum Mechanics

Cited by in corpus (3)

• Mathematical and physical aspects of complex symmetric operators
• Extension of the $CPT$ Theorem to non-Hermitian Hamiltonians and Unstable States
• On S-matrix of Schrodinger Operators with Non-Symmetric Zero-Range Potentials