Physics Master of Science Research Project by Eamon Lyons
Advisor: Dr. Jay Wang, Department of Physics
Abstract:
Our research seeks to examine the effects of altering boundary conditions of otherwise analytical quantum systems and examining the efficacy of Perturbation Theory at modeling this compared to numerical results. Starting with the standard “infinite square well” we add a linear potential $\beta x$ (where $\beta$ is a real, positive constant). Using Perturbation Theory, we found the first order energy correction which, when combined with the unperturbed energy, gives a decent approximation for our energy states at low $\beta$ value. Using numerical methods, we were able to increase the accuracy of our energy values. Plotting the wavefunction reveals some expected results, such as a much greater likelihood of the particle being closer to the bottom of the well for the ground state. There were also some unexpected results such as higher energy states having a global maximum higher up in the well.
Note: All PHY Graduate Students are encouraged to attend. Open to the public. All interested parties are invited to attend.
SENG 201
Dr. Jay Wang
jwang@umassd.edu