Accuracy on eigenvalues for a Schrodinger operator with a degenerate potential in the semi-classical limit
Mathematical Physics
2008-12-17 v1 math.MP
Abstract
We consider a semi-classical Schrodinger operator with a degenerate potential V(x,y) =f(x) g(y) . g is assumed to be a homogeneous positive function of m variables and f is a strictly positive function of n variables, with a strict minimum. We give sharp asymptotic behaviour of low eigenvalues bounded by some power of the parameter h, by improving Born-Oppenheimer approximation.
Cite
@article{arxiv.math-ph/0606032,
title = {Accuracy on eigenvalues for a Schrodinger operator with a degenerate potential in the semi-classical limit},
author = {Abderemane Morame and Francoise Truc},
journal= {arXiv preprint arXiv:math-ph/0606032},
year = {2008}
}