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

Abderemane Morame (1) , Francoise Truc (2)

1 LMJL - Laboratoire de Mathématiques Jean Leray
2 IF - Institut Fourier

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.

Keywords: eigenvalues; semi-classical asymptotics; Born-Oppenheimer approximation

Domains: Mathematical Physics [math-ph]; Mathematical Physics [math-ph]

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⟩