ABSTRACT
This chapter focuses on how molecular systems evolve in time without any applied field, “field-free dynamics”. It outlines an approach for solving the time-dependent Schrödinger equation (TDSE) numerically, and makes use of the split-operator method since it is intuitive, physical, and simple to implement. The chapter develops an intuitive understanding of field-free quantum dynamics in one dimension. It accomplishes this by interpreting numerical solutions to the TDSE. Many analytic solutions rely on a time-independent approach, which is not always the most useful basis for understanding the dynamics. The chapter discusses wave packet dynamics in a finite, square well. It considers an initial Gaussian wave function localized near the center of the well. The quantum energy distribution in a bound potential well is discrete, while the classical energy distribution is continuous. The chapter considers wave function dynamics in an anharmonic Morse potential, which serves as a good approximation for many molecular bonds.
