| dc.description.abstract | In quantum mechanics, the propagator specifies the probability amplitude for a particle to travel from one position in space to another in a given period of time. Utilizing a propagator, as well as a basic Gaussian wave packet, one can integrate the two quantities against one another to construct a full quantum wave function — a function that describes the behavior of a quantum particle. Using previously computed propagators, we present a visual representation of this semi- classical wave packet behavior for a particle interacting with a ‘ceiling’ boundary. We explain the roles of the parameters embedded in the Gaussian wave packets and examine their effects on the resulting wave function. Two different types of propagator expressions have been derived, one in terms of initial position data and another in terms of initial momentum data. We present results computed by both methods and elaborate upon the regimes in which one particular method is preferred. Additionally, we present the software developed to conduct this research and detail how it is used such that it may be adapted for future use. | |
