The UTC Graduate School is pleased to announce that Samantha Craig will present Master's research titled, Applying the Time-Independent Schrodinger Equation to Dirac Delta Potentials in an Infinite Potential Well on 03/03/2025 at 11:15 AM in Lupton 391. Everyone is invited to attend. 

Mathematics

Chair: Boris Belinskiy

Co-Chair: 

Abstract:

The infinite potential well is one of the most well-known systems in quantum mechanics. Additionally, the Dirac Delta potential is also well studied, but less so in the context of an infinite potential well system. By applying such a potential function to the time-independent Schrodinger equation, the typical boundary conditions for an infinite well and normalization conditions are used to obtain the wave function \psi(x). The system naturally imposes an additional condition at \psi(0) due to the Dirac Delta function, which yields the relation that gives the infinite set of allowed energy values {E_n}. These results were then applied to a lattice potential within the infinite well, which is defined as a finite sum of Dirac Delta functions that are spread evenly within the bounds of the well. For future work, more numerical analysis may be done on these systems, as well as expanding the problem to two dimensions.