Share Email Print
cover

Proceedings Paper

Adaptive numerical methods for the time-dependent Schrödinger equation in atomic and laser physics
Author(s): Vladimir L. Derbov; M. S. Kaschiev; V. V. Serov; A. A. Gusev; S. I. Vinitsky
Format Member Price Non-Member Price
PDF $14.40 $18.00
cover GOOD NEWS! Your organization subscribes to the SPIE Digital Library. You may be able to download this paper for free. Check Access

Paper Abstract

Stable adaptive methods for solving the time-dependent Schrodinger equation (TDSE)) are considered in the framework of conventional finite-element representation of smooth solutions over coordinate spaces of a projective type with long derivatives. Generalization of Cranck-Nicholson scheme of forth order in time step is implemented. Projective “hidden variable” representation of strongly oscillating solutions is realized to extract explicitly the strongly variable gauge phase factor and to evaluate only the “pilot solution” which is reduced to a smooth envelope of the solution under consideration. Such an approach corresponds to the known transformation from Euler space variables to Lagrangian ones and the inducing characteristic representation of self-similar solutions widely used in the flow propagation problems. We study both smooth and strongly oscillating solutions of TDSE describing conventional atomic models in the laser pulse field. It is shown that for short-range potentials the “pilot solution” can be naturally interpreted as the spectrum of the outgoing wave. The examples considered show the efficiency and stability of the elaborated methods.

Paper Details

Date Published: 23 September 2003
PDF: 9 pages
Proc. SPIE 5067, Saratov Fall Meeting 2002: Laser Physics and Photonics, Spectroscopy, and Molecular Modeling III; Coherent Optics of Ordered and Random Media III, (23 September 2003); doi: 10.1117/12.518608
Show Author Affiliations
Vladimir L. Derbov, Saratov State Univ. (Russia)
M. S. Kaschiev, Institute of Mathematics and Informatics (Bulgaria)
V. V. Serov, Saratov State Univ. (Russia)
A. A. Gusev, Joint Institute for Nuclear Research (Russia)
S. I. Vinitsky, Joint Institute for Nuclear Research (Russia)


Published in SPIE Proceedings Vol. 5067:
Saratov Fall Meeting 2002: Laser Physics and Photonics, Spectroscopy, and Molecular Modeling III; Coherent Optics of Ordered and Random Media III
Dmitry A. Zimnyakov; Vladimir L. Derbov; Leonid A. Melnikov; Lev M. Babkov, Editor(s)

© SPIE. Terms of Use
Back to Top