Student: Matt Kohut

Advisors:

Dr. Ovidiu Costin and Dr. Rodica Costin (Rutgers Math Department)

`For more information on my project, please see Michael
Grabchak's page.`

Methodology: Our method will be to analyze solutions to an instance of Schrodinger's Equation, which is the governing equation for quantum mechanical systems. Schrodinger's Equation gives the wave function of the particle, which is essentially a probability density function for the system at a time t (so integrating the wave function over a subset of the real line for a fixed t gives the probability of finding the particle in that set at time t). Given initial conditions, we'll show that our particular wave function goes to zero as time goes to infinity (which is equivalent to saying that ionization has occurred). In order to study the long term time dependence of the wave function (that is, to study the growth order), we will take the Laplace Transform of Schrodinger's Equation and instead study the analyticity of the Laplace Transformed Wave Function. This method is justified if one notes that Laplace Transforms turn multiplication into differentiation (in a sense).