Algebraic method for the evolution operator approximation

Abstract

The approximation of a short-time evolution operator for a molecular system with the Hamiltonian is constructed in terms of the evolution operator of an unperturbed system, a perturbative potential V and commutators of and V. A description of a powerful method for such a construction based on the Lie-algebra technique is given. It is demonstrated that efficient representation for the evolution operator can be obtained using approximations like where . This relation is accurate up to the third order in time. The simplest approximations of this type are listed.