Exponentially accurate error estimates of quasiclassical eigenvalues

JULIO H. TOLOZA

JOURNAL OF PHYSICS. A - MATHEMATICAL AND GENERAL

Institute of Physics Publishing

Lugar: Bristol; Año: 2001 vol. 34 p. 1203 - 1218

0305-4470

We study the behaviour of truncated Rayleigh-Schrödinger series for the low-lying eigenvalues of the one-dimensional, time-independent Schrödinger equation, in the semiclassical limit h->0. Under certain hypotheses on the potential V(x), we prove that for any given small h>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/h)$ for some positive constant C. We also prove the analogous results concerning the eigenfunctions.