Research Article Open Access

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

Sabria Bouheroum-Mentri and Amina Benbernou

Abstract

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.

Journal of Mathematics and Statistics
Volume 3 No. 2, 2007, 70-76

DOI: https://doi.org/10.3844/jmssp.2007.70.76

Submitted On: 20 December 2006 Published On: 30 June 2007

How to Cite: Bouheroum-Mentri, S. & Benbernou, A. (2007). A Priori Estimation of the Resolvent on Approximation of Born-Oppenheimer. Journal of Mathematics and Statistics, 3(2), 70-76. https://doi.org/10.3844/jmssp.2007.70.76

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Keywords

  • Distorsion
  • eigenvalues
  • estimation
  • resolvent
  • resonances