 00395 Julio H. Toloza
 Exponentially Accurate Error Estimates of Quasiclassical Eigenvalues
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Oct 4, 00

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Abstract. We study the behaviour of truncated RayleighSchr\"odinger series for
the lowlying eigenvalues of the onedimensional, timeindependent
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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