Application of the Fourier-Gauss transform to the Cauchy problem for the Schroedinger equation: theoretical consideration of the numerical algorithm
Keywords:
нестационарное уравнение Шредингера, гауссовы волновые пакеты, преобразование Фурье-Гаусса, задача Коши, численные методы, устойчивость, сходимостьAbstract
The theoretical justification of the earlier proposed numerical procedure for solving the Scroedinger equation by the Fourier-Gauss transform is given. Some sufficient conditions for the equation (potential) and initial states to make the method applicable are investigated.
References
- Арсеньев А.А. Оценка функции Грина оператора Шредингера // Теор. и матем. физ. 1998. 115, № 1. 85-92.
- Hagedorn G.A. Raising and lowering operators for semiclassical wave packets // Ann. Phys. 1998. 269. 77-104.
- Hagedorn G.A., Joye A. Exponentially accurate semiclassical dynamics: propagation, localization, Ehrenfest times, scattering and more general states // Ann. Henri Poincaré. 2000. 1. 837-883.
- Айдагулов Г.Р. Применение преобразования Фурье-Гаусса к решению задачи Коши для уравнения Шредингера // ЖВМиМФ. 2002. 42, № 12. 1810-1815.
- Folland G.B. Harmonic analysis in phase space. Princeton: Princeton Univ., 1989.
- Чуи К. Введение в вэйвлеты. М.: Мир, 2001.
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Published
27-05-2003
How to Cite
Айдагулов Г. Application of the Fourier-Gauss Transform to the Cauchy Problem for the Schroedinger Equation: Theoretical Consideration of the Numerical Algorithm // Numerical Methods and Programming (Vychislitel’nye Metody i Programmirovanie). 2003. 4. 183-187
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Section
Section 1. Numerical methods and applications