Semiclassical eigenvalue asymptotics for a Schrödinger operator with a degenerate potential

Article type: Research Article

Authors: Morame, Abderemane | Truc, Françoise

Affiliations: Université de Nantes, Faculté des Sciences, Dpt. Mathématiques, UMR 6629 du CNRS, B.P. 99208, 44322 Nantes Cedex 3, France E‐mail: [email protected]‐nantes.fr | Université de Grenoble I, Institut Fourier, UMR 5582 CNRS‐UJF, B.P. 74, 38402 St Martin d’Hères Cedex, France E‐mail: Francoise.Truc@ujf‐grenoble.fr

Abstract: We give the asymptotic behaviour, when h tends to zero, of the number of eigenvalues less then a fixed energy \lambda, of the Schrödinger operator {\widehat{H}_h}=-h^2\Delta + f(x)g(y),\ (x,y)\in \mathbf{R}^d=\mathbf{R}^n\times \mathbf{R}^m. f and g are continuous and positive functions tending to infinity at infinity, g(y) is homogeneous and f(x)>0.

Journal: Asymptotic Analysis, vol. 22, no. 1, pp. 39-49, 2000