Algorithm for reduction of boundary-value problems in multistep adiabatic approximation
Abstract
The adiabatic approximation is well-known method for effective study of few-body systems in molecular, atomic and nuclear physics, using the idea of separation of "fast" and "slow" variables. The generalization of the standard adiabatic ansatz for the case of multi-channel wave function when all variables treated dynamically is presented. For this reason we are introducing the step-by-step averaging methods in order to eliminate consequently from faster to slower variables. We present a symbolic-numerical algorithm for reduction of multistep adiabatic equations, corresponding to the MultiStep Generalization of Kantorovich Method, for solving multidimensional boundary-value problems by finite element method. An application of the algorithm to calculation of the ground and first exited states of a Helium atom is given.
Keywords
Cite
@article{arxiv.1005.2089,
title = {Algorithm for reduction of boundary-value problems in multistep adiabatic approximation},
author = {A. A. Gusev and O. Chuluunbaatar and V. P. Gerdt and B. L. Markovski and V. V. Serov and S. I. Vinitsky},
journal= {arXiv preprint arXiv:1005.2089},
year = {2015}
}
Comments
7 figures; Submitted to Mathematics and Computer in Simulation