PT-Symmetric Schrödinger Operators with Unbounded Potentials

2011
ISBN: 978-3-8348-1762-4
Verlag: Vieweg+Teubner Verlag

Buch, Englisch, 83 Seiten, Format (B × H): 148 mm x 210 mm, Gewicht: 146 g

Following the pioneering work of Carl M. Bender et al. (1998), there has been an increasing interest in theoretical physics in so-called PT-symmetric Schrödinger operators. In the physical literature, the existence of Schrödinger operators with PT-symmetric complex potentials having real spectrum was considered a surprise and many examples of such potentials were studied in the sequel. From a mathematical point of view, however, this is no surprise at all – provided one is familiar with the theory of self-adjoint operators in Krein spaces.
Jan Nesemann studies relatively bounded perturbations of self-adjoint operators in Krein spaces with real spectrum. The main results provide conditions which guarantee the spectrum of the perturbed operator to remain real. Similar results are established for relatively form-bounded perturbations and for pseudo-Friedrichs extensions. The author pays particular attention to the case when the unperturbed self-adjoint operator has infinitely many spectral gaps, either between eigenvalues or, more generally, between separated parts of the spectrum.

Zielgruppe

Researchers and students of mathematics, especially those interested in the spectral theory of linear operators in Krein spaces.

Autoren/Hrsg.

Nesemann, Jan

Fachgebiete

• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
• Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis
• Naturwissenschaften Physik Quantenphysik

Inhaltsverzeichnis

Linear Operators in Krein Spaces – PT-Symmetry – Spectral Theory – Relatively Bounded/Compact Perturbations – Relatively Form-Bounded/Form-Compact Perturbations – Schrödinger Operators

Über Autor(innen)

Dr. Jan Nesemann holds a master’s degree in mathematics as well as in business administration. He received his PhD in mathematics from the University of Bern under the guidance of Prof. Dr. Christiane Tretter. Currently he works as an actuarial and financial services consultant in Zurich.