Semiclassical initial value representation propagation of vibrational wave functions

Abstract

Two new, uniform, semiclassical initial value representation (IVR) expressions are obtained for the time-dependent wave function Ψt(x) that evolves from the eigenstate ψ(x) of a “zero-order” Hamiltonian describing an arbitrary, integrable, vibrational system. In contrast to most other IVR approaches, this initial state is, itself, treated semiclassically so that it need not be determined by independent quantum calculations. One of the IVR expressions presented here describes Ψt(x) as an integral over only half of the phase space variables of the system, so that it holds the promise of computational advantages over existing treatments that involve integrations over all of phase space. Numerical tests confirm the efficiency and accuracy of the semiclassical approximations.