George A. Hagedorn and Alain Joye
Elementary Exponential Error Estimates for the Adiabatic Approximation
(31K, latex)

ABSTRACT.  We present an elementary proof that the quantum adiabatic approximation 
is correct up to exponentially small errors for Hamiltonians that depend 
analytically on the time variable. Our proof uses optimal truncation of 
a straightforward asymptotic expansion. We estimate the terms of the 
expansion with standard Cauchy estimates.