Evolution time and energy uncertainty

Timothy Boykin, Department of Electrical and Compute Engineering, The University of Alabama in Huntsville
Neerav Kharche, Birck Nanotechnology Center and Purdue University
Gerhard Klimeck, Purdue University

Abstract

Often one needs to calculate the evolution time of a state under a Hamiltonian with no explicit time dependence when only numerical methods are available. In cases such as this, the usual application of Fermi's golden rule and first-order perturbation theory is inadequate as well as being computationally inconvenient. Instead, what one needs are conditions under which the evolution time may be obtained from the easily calculated energy uncertainty. This work derives some general conditions for obtaining the evolution time from the energy uncertainty.