61 research outputs found
Towards theory of C-symmetries
The concept of C-symmetry originally appeared in PT-symmetric quantum
mechanics is studied within the Krein spaces framework
Lax-Phillips scattering theory for PT-symmetric \rho-perturbed operators
The S-matrices corresponding to PT-symmetric \rho-perturbed operators are
defined and calculated by means of an approach based on an operator-theoretical
interpretation of the Lax-Phillips scattering theory
Singularly Perturbed Self-Adjoint Operators in Scales of Hilbert spaces
Finite rank perturbations of a semi-bounded self-adjoint operator A are
studied in the scale of Hilbert spaces associated with A. A concept of
quasi-boundary value space is used to describe self-adjoint operator
realizations of regular and singular perturbations of A by the same formula. As
an application the one-dimensional Schr\"{o}dinger operator with generalized
zero-range potential is considered in the Sobolev space W^p_2(\mathbb{R}),
p\in\mathbb{N}.Comment: 26 page
PT Symmetric, Hermitian and P-Self-Adjoint Operators Related to Potentials in PT Quantum Mechanics
In the recent years a generalization of the
harmonic oscillator using a complex deformation was investigated, where
\epsilon\ is a real parameter. Here, we will consider the most simple case:
\epsilon even and x real. We will give a complete characterization of three
different classes of operators associated with the differential expression H:
The class of all self-adjoint (Hermitian) operators, the class of all PT
symmetric operators and the class of all P-self-adjoint operators.
Surprisingly, some of the PT symmetric operators associated to this expression
have no resolvent set
- …