Journal of Mathematics and Statistics

A Priori Estimation of the Resolvent on Approximation of Born-Oppenheimer

Sabria Bouheroum-Mentri and Amina Benbernou

DOI : 10.3844/jmssp.2007.70.76

Journal of Mathematics and Statistics

Volume 3, Issue 2

Pages 70-76


In this study, we estimate the resolvent of the two bodies Shrodinger operator perturbed by a potential of Coulombian type on Hilbert space when h tends to zero. Using the Feschbach method, we first distorted it and then reduced it to a diagonal matrix. We considered a case where two energy levels cross in the classical forbidden region. Under the assumption that the second energy level admits a non degenerate point well and virial conditions on the others levels, a good estimate of the resolvent were observed.


© 2007 Sabria Bouheroum-Mentri and Amina Benbernou. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.