PT Symmetric Schrödinger Operators: Reality of the Perturbed Eigenvalues

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2010
• Main Authors: Caliceti, E., Cannata, F., Graffi, S.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2010
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/146116
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: PT Symmetric Schrödinger Operators: Reality of the Perturbed Eigenvalues / E. Caliceti // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 22 назв. — англ.

We prove the reality of the perturbed eigenvalues of some PT symmetric Hamiltonians of physical interest by means of stability methods. In particular we study 2-dimensional generalized harmonic oscillators with polynomial perturbation and the one-dimensional x²(ix)ⁿ for −1<n<0.