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This article is cited in 10 scientific papers (total in 10 papers)
Singular perturbation of polynomial potentials with applications to $PT$-symmetric families
Alexandre Eremenko, Andrei Gabrielov Purdue University, West Lafayette, IN, USA
Abstract:
We discuss eigenvalue problems of the form $-w''+Pw=\lambda w$ with complex polynomial potential $P(z)=tz^d+\ldots$, where $t$ is a parameter, with zero boundary conditions at infinity on two rays in the complex plane. In the first part of the paper we give sufficient conditions for continuity of the spectrum at $t=0$. In the second part we apply these results to the study of topology and geometry of the real spectral loci of $PT$-symmetric families with $P$ of degree 3 and 4, and prove several related results on the location of zeros of their eigenfunctions.
Key words and phrases:
singular perturbation, Schrödinger operator, eigenvalue, spectral determinant, $PT$-symmetry.
Citation:
Alexandre Eremenko, Andrei Gabrielov, “Singular perturbation of polynomial potentials with applications to $PT$-symmetric families”, Mosc. Math. J., 11:3 (2011), 473–503
Linking options:
https://www.mathnet.ru/eng/mmj428 https://www.mathnet.ru/eng/mmj/v11/i3/p473
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Abstract page: | 284 | Full-text PDF : | 1 | References: | 48 |
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