Emanuela Caliceti, Francesco Cannata, Sandro Graffi, “<nobr>$\mathcal P\mathcal T$</nobr> Symmetric Schrödinger Operators: Reality of the Perturbed Eigenvalues”, SIGMA, 2010, Volume 6,009, 8 pp.

This article is cited in 9 papers

$\mathcal P\mathcal T$ Symmetric Schrödinger Operators: Reality of the Perturbed Eigenvalues

Emanuela Caliceti^a, Francesco Cannata^b, Sandro Graffi^a

^a Dipartimento di Matematica, Università di Bologna, and INFN, Bologna, Italy
^b INFN, Via Irnerio 46, 40126 Bologna, Italy

Abstract: We prove the reality of the perturbed eigenvalues of some $\mathcal P\mathcal T$ 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 $x^2(ix)^\epsilon$ for $-1<\epsilon<0$.

Keywords: $\mathcal P\mathcal T$ symmetry; real spectra; perturbation theory.

MSC: 47A55; 47A75; 81Q15; 34L40; 35J10

Received: November 3, 2009; in final form January 14, 2010; Published online January 20, 2010

Language: English

DOI: 10.3842/SIGMA.2010.009