Abstract

In this paper we study the bottom of the spectrum of a semiclassical Schrodinger operator Pm (h) = (h2 /2 )Am + Vm in high dimension m. We assume that Vm is convex and satisfies some conditions uniformly with respect to m. We get a complete asymptotic expansion in powers of h with an explicit control of the coefficients and of the remainder terms with respect to m of its lowest eigenvalue and we show that its first eigenfunctions decays exponentially outside a £2 -ball of radius ...;m centered at the point where Vm reaches its minimum, as h -+ O.

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