Mathematical and Computational Methods in Quantum Chemistry

An Approximate Semiclassical Method that Uses Real Valued Trajectories for Time Dependent Tunneling Calculations

Michael Herman

Tulane University


A semiclassical method will be presented that describes the time dependent tunneling of a quantum wavepacket encountering a barrier. Tunneling through barriers play a significant role in many reactions. The method described in this talk uses an approximation to the standard semiclassical stationary phase method. The approximation employed in this work leads to real valued tunneling trajectories, while most methods for this problem employ complex valued trajectories. Using only real valued trajectories will have significant advantages in applications to larger systems. It is found that there are typically three of these approximate stationary phase contributions to the wave function for each point r in the transmitted region. Two of these have energies very close to the barrier top, one slightly above the barrier top and the other slightly below it. The third approximate stationary phase contribution is at a lower energy. Difficulties in obtaining accurate values for the contributions from trajectories with an energy very close to the barrier top will be considered, and the accuracy of the approximate stationary phase wave function will be discussed.