TY  - JOUR
AU  - Bouheroum-Mentri, Sabria 
AU  - Benbernou, Amina 
PY  - 2007
TI  - A Priori Estimation of the Resolvent on Approximation of Born-Oppenheimer
JF  - Journal of Mathematics and Statistics
VL  - 3
IS  - 2
DO  - 10.3844/jmssp.2007.70.76
UR  - https://thescipub.com/abstract/jmssp.2007.70.76
AB  - 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.