Title: ПРАВИЛА ОФОРМЛЕНИЯ ТЕЗИСОВ КОНФЕРЕНЦИИ ВНКСФ-7
Author: Sergey Trapeznikov
Last saved by: Андрей
Company: Saint-Petersburg State University

Специализация: 010700/17 Теоретическая и математическая физика
Программа: 25 Методы и проблемы математической и вычислительной физики
Руководитель программы: проф., д.ф.-м.н. Т.А. Суслина
Кафедра высшей математики и математической физики
Научный руководитель: доц., д.ф.-м.н. А.А. Федотов
Рецензент: проф., д.ф.-м.н. Д.Р. Яфаев

Linear adiabatic dynamics generated by operators with continuous spectrum. Schrödinger operator
A. B. Smirnov

The asymptotic behavior of the solution to the Cauchy problem for the one-dimensional non-stationary Schrödinger equation with a slowly varying potential is studied.  We consider smooth and rapidly decaying potentials. The initial condition is chosen so that the solution of the free Schrödinger equation is smooth and grows not faster than a polynomial at infinity. 
 We develop a recurrent procedure to construct the adiabatic asymptotics of the solution of the problem. We apply our approach to analyze in details the solution in two different cases: in the case when the initial condition is a rapidly decaying function and in the case when it is an oscillating exponent.

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