Application of the Fourier-Gauss transform to the Cauchy problem for the Schroedinger equation: theoretical consideration of the numerical algorithm

Authors

  • G.R. Aidagulov Lomonosov Moscow State University

Keywords:

нестационарное уравнение Шредингера, гауссовы волновые пакеты, преобразование Фурье-Гаусса, задача Коши, численные методы, устойчивость, сходимость

Abstract

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.

Author Biography

G.R. Aidagulov

References

  1. Арсеньев А.А. Оценка функции Грина оператора Шредингера // Теор. и матем. физ. 1998. 115, № 1. 85-92.
  2. Hagedorn G.A. Raising and lowering operators for semiclassical wave packets // Ann. Phys. 1998. 269. 77-104.
  3. 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.
  4. Айдагулов Г.Р. Применение преобразования Фурье-Гаусса к решению задачи Коши для уравнения Шредингера // ЖВМиМФ. 2002. 42, № 12. 1810-1815.
  5. Folland G.B. Harmonic analysis in phase space. Princeton: Princeton Univ., 1989.
  6. Чуи К. Введение в вэйвлеты. М.: Мир, 2001.

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

Issue

Section

Section 1. Numerical methods and applications