Conference publications

Semi-classical Spectrum of the Schrödinger Operator with the Complex Potential

Esina A. I.

"Математика. Компьютер. Образование". Cб. трудов XVI международной конференции. Под общей редакцией Г.Ю. Ризниченко Ижевск: Научно-издательский центр "Регулярная и хаотическая динамика", 2009. Vol. 2. Pp. 46-48. (accepted)

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In this work we investigated spectrum of $H(x, - ih\frac{d}{{dx}}) = - h^2 \frac{{d^2 }}{{dx^2 }} + i(\cos x + \cos 2x)$ operator at $h \to 0$ (semi-classical limit) using Stokes lines technique. Computer-aided calculations were an important part of the work. We obtained equations for points of the spectrum and spectral graph. Points of the spectrum of the operator considered are in the $O(h^2)$ neighborhood of the spectral graph.

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