01-397 Julio H. Toloza

Exponentially Accurate Error Estimates of Quasiclassical Eigenvalues II: Several Dimensions (437K, Postscript) Oct 24, 01

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Abstract. We study the behavior of truncated Rayleigh-Schr\"odinger series for low-lying eigenvalues of the time-independent Schr\"odinger equation, in the semiclassical limit $\hbar\searrow 0$. In particular we prove that if the potential energy satisfies certain conditions, there is an optimal truncation of the series for the eigenvalues, in the sense that this truncation is exponentially close to the exact eigenvalue. These results were already discussed for one-dimensional case in a previous paper. This time we consider the several dimensional case, where degeneracy plays a central role.

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