Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 6 (2010), 009, 8 pages      arXiv:1001.3656
Contribution to the Proceedings of the 5-th Microconference Analytic and Algebraic Methods V

PT Symmetric Schrödinger Operators: Reality of the Perturbed Eigenvalues

Emanuela Caliceti a, Francesco Cannata b and Sandro Graffi a
a) Dipartimento di Matematica, Università di Bologna, and INFN, Bologna, Italy
b) INFN, Via Irnerio 46, 40126 Bologna, Italy

Received November 03, 2009, in final form January 14, 2010; Published online January 20, 2010

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)ε for −1<ε<0.

Key words: PT symmetry; real spectra; perturbation theory.

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