Accuracy on eigenvalues for a Schrodinger operator with a degenerate potential in the semi-classical limit

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.
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Submitted on : Friday, June 9, 2006 - 1:29:47 PM
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Abderemane Morame, Francoise Truc. Accuracy on eigenvalues for a Schrodinger operator with a degenerate potential in the semi-classical limit. Cubo, a Mathematical Journal, 2007, 9 (2), pp.1-15. ⟨hal-00079167⟩

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