Semiclassical analysis of low lying eigenvalues. I. Non-degenerate minima: asymptotic expansions
نویسنده
چکیده
We consider eigenvalues of Schrodinger operators of the form ~ + ~,2h + ~?g where h >0 has finitely many minima, each of which is non-degenerate. We prove a folk theorem about the asymptotic behavior of the nth eigenvalue in the ~, -~ oo limit. We conclude with a few remarks about the extension to Riemannian manifolds because of the significance to Witten’s proof of the Morse inequalities. RESUME. On considere les valeurs propres d’operateurs de Schrodinger de la forme 0394 + + 03BBg où h ~ 0 a un nombre fini de minima, tous non degeneres. On demontre un resultat generalement admis sur Ie comportement asymptotique de la rie"’e valeur propre dans la limite ou i cc. On conclut par quelques remarques sur 1’extension du resultat a des varietes riemanniennes, en raison de son role dans la demonstration par Witten des inegalites de Morse.
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