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Center for Nonlinear Studies |
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. For instance, coupled electron-proton tunneling is an important mechanism in many isomerization reactions involving organic compounds. The method described in this talk uses an approximation to the standard semiclassical stationary phase method. A discussion of semiclassical methods and the stationary phase approximation will be provided in the introduction to the talk. 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 system. 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.
Host: Travis Peery