Wavepacket Propagation in the Determination of Microscopic Eigenenergies: I: The Spectral Method

Abstract

Examining the relationship between chemical structure and dynamics should be fundamental to the undergraduate study of microscopic systems. With this in mind wavepacket propagation, which is traditionally used in application to dynamical problems, is used here as the foundation for determining eigenenergies. The system is propagated in space and time from an initial wavepacket as in a traditional dynamical study. We then proceed to determine eigenenergies from the appearance of resonances in a spectrum of energies that is generated from the spatial projection of the wavepacket onto the initial wavepacket. Application of the spectral method is made to a classic electronic structure problem; resonances are observed at energies which match the known energy structure of the problem. Finally, the relevance of wavepacket propagation to the elucidation of structure and dynamics at the undergraduate level is discussed.