- 00-395 Julio H. Toloza
- Exponentially Accurate Error Estimates of Quasiclassical Eigenvalues
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.