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This article is cited in 9 scientific papers (total in 9 papers)
$\mathcal P\mathcal T$ Symmetric Schrödinger Operators: Reality of the Perturbed Eigenvalues
Emanuela Calicetia, Francesco Cannatab, Sandro Graffia 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.
Received: November 3, 2009; in final form January 14, 2010; Published online January 20, 2010
Citation:
Emanuela Caliceti, Francesco Cannata, Sandro Graffi, “$\mathcal P\mathcal T$ Symmetric Schrödinger Operators: Reality of the Perturbed Eigenvalues”, SIGMA, 6 (2010), 009, 8 pp.
Linking options:
https://www.mathnet.ru/eng/sigma466 https://www.mathnet.ru/eng/sigma/v6/p9
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Abstract page: | 470 | Full-text PDF : | 65 | References: | 54 |
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