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

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

2006-06-09

arxiv.org/abs/math-ph/0606032v1

Cubo, a Mathematical Journal 9, 2 (2007) 1-15

Physics

Mathematical Physics

Scientific paper

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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