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Conference publications

Quasiclassical Spectrum of Schrödinger’s Operator with the Complex Potential

Esina A. I.

"Математика. Компьютер. Образование". Cб. трудов XV международной конференции. Под общей редакцией Г.Ю. Ризниченко Ижевск: Научно-издательский центр "Регулярная и хаотическая динамика", 2008. Vol. 2, 276pp. Pp. 219-228. (accepted)

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Let’s investigate equation $- h^2 y'' + i*V(x)y = Ey$. Where $h$-real parameter and $V(x) = Cos(x) + Cos(2x)$. When parameter $h$ is fixed, question ‘With what $E$ this equation has an answer is a question ‘What kind of spectrum has an operator $H(x, - ih\frac{\partial }{{\partial x}}) = - h^2 \frac{{\partial ^2 }}{{\partial x^2 }} + i*V(x)$. We are interested in asymptotic of this operator with $h \to 0$. In physics this limit is a limit of transit from quantum system to classical system



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