00-395 Julio H. Toloza

Exponentially Accurate Error Estimates of Quasiclassical Eigenvalues (271K, Postscript) Oct 4, 00

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Abstract. We study the behaviour of truncated Rayleigh-Schr\"odinger series for the low-lying eigenvalues of the one-dimensional, time-independent Schr\"odinger equation, in the semiclassical limit $\hbar\rightarrow 0$. Under certain hypotheses on the potential $V(x)$, we prove that for any given small $\hbar>0$ there is an optimal truncation of the series for the approximate eigenvalues, such that the difference between an approximate and exact eigenvalue is smaller than $\exp(-C/\hbar)$ for some positive constant $C$. We also prove the analogous results concerning the eigenfunctions.

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