00-395 Julio H. Toloza
Exponentially Accurate Error Estimates of Quasiclassical Eigenvalues (271K, Postscript) Oct 4, 00
Abstract , Paper (src), View paper (auto. generated ps), Index of related papers

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.

Files: 00-395.src( 00-395.comments , 00-395.keywords , estimate_iop.ps )