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$\mathcal P\mathcal T$ Symmetric Schrödinger Operators: Reality of the Perturbed Eigenvalues
Symmetry, integrability and geometry: methods and applications, Tome 6 (2010) Cet article a éte moissonné depuis la source Math-Net.Ru

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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 $-1\epsilon0$.
Keywords: $\mathcal P\mathcal T$ symmetry; real spectra; perturbation theory. 
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     author = {Emanuela Caliceti and Francesco Cannata and Sandro Graffi},
     title = {$\mathcal P\mathcal T$ {Symmetric} {Schr\"odinger} {Operators:} {Reality} of the {Perturbed} {Eigenvalues}},
     journal = {Symmetry, integrability and geometry: methods and applications},
     year = {2010},
     volume = {6},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2010_6_a8/}
}
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Emanuela Caliceti; Francesco Cannata; Sandro Graffi. $\mathcal P\mathcal T$ Symmetric Schrödinger Operators: Reality of the Perturbed Eigenvalues. Symmetry, integrability and geometry: methods and applications, Tome 6 (2010). http://geodesic.mathdoc.fr/item/SIGMA_2010_6_a8/

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