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Symmetry, Integrability and Geometry: Methods and Applications, 2010, Volume 6, 009, 8 pp.
DOI: https://doi.org/10.3842/SIGMA.2010.009 (Mi sigma466) 		 
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
Full-text PDF (221 kB) Citations (9)
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DOI: https://doi.org/10.3842/SIGMA.2010.009
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
Bibliographic databases:
Document Type: Article
MSC: 47A55; 47A75; 81Q15; 34L40; 35J10
Language: English
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.
Citation in format AMSBIB
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\by Emanuela Caliceti, Francesco Cannata, Sandro Graffi
\paper $\mathcal P\mathcal T$ Symmetric Schr\"odinger Operators: Reality of the Perturbed Eigenvalues
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\papernumber 009
\totalpages 8
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    • This publication is cited in the following 9 articles:
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    		Symmetry, Integrability and Geometry: Methods and Applications
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