# PHY Theses

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Item The magnetic vector potential, Klein-Gordon equation and Klein’s paradox in relativistic quantum mechanics(2007-05) Schaffer, David L.; Behrman, Elizabeth C.This thesis evaluates solutions to the Klein-Gordon equation with scalar and vector potentials in the Symmetric and Landau gauges. The solution for the Klein-Gordon equation in the Symmetric gauge does reproduce elements of the two dimensional quantum harmonic oscillator. The Landau gauge solution is used in the velocity selector situation where particles can have acceleration free motion for a selected velocity. The Klein Paradox for spin less particles is reviewed and its application to the Klein- Gordon equation shows that the vector potential can have an effect on particle pair production without the violation of conservation of momentum or energy, that this effect is to suppress the particle pair production associated with Klein’s paradox and that the suppressive effect can, under certain conditions, become strong enough to prevent particle pair production in Klein’s paradox when the scalar potential is otherwise many times what would be necessary to create Klein’s paradox particle pairs.Item Calculation of quantum entanglement using a genetic algorithm(2007-05) Lesniak, Joseph; Behrman, Elizabeth C.Quantum entanglement is a multifaceted property that has attracted much attention, since it is used as the basis for such applications as quantum cryptography, quantum teleportation, and quantum computing. The calculation of quantum entanglement therefore has gained importance. As systems that use entanglement have evolved, the calculation of entanglement has become much more complex. A general method was developed for the calculation of entanglement for n-qubit or n-qudit system, based on the relative entropy of entanglement, and using a genetic algorithm technique. The method was tested on a two qubit system, for which there are some known points, and compared to exact calculations using the entanglement of formation and to another approximate method based on a quantum neural network. Advantages and disadvantages of the method and future work are discussedItem Effective medium theory and Rosseland mean opacity(2005-12) Penley, Jonathan Jay; Ferguson, Jason W.As a gas cools the mean opacity becomes dominated by the opacity of molecules and at low temperatures solid dust grains. Accurately computing the opacity is necessary to accurately compute the transfer of radiation through a gas. An attempt is made to refine the calculation of opacity within the stellar atmosphere modeling program PHOENIX through the addition of new optical constants, including those of the mineral species enstatite, forsterite, and fayalite. A general search for laboratory measurements of the optical constants of these minerals was performed, as well as a comparative study of the various data sets found. A study is also made investigating the importance of effective medium theory in the calculation of mean opacities within PHOENIX. Effective medium theory details the study of complex porous grains and the way in which they interact with electromagnetic radiation. The results of applying effective medium theory to modify the optical constants already within the bounds of this study are then compared to the current processes within PHOENIX. This study concludes that adding optical constants for forsterite and fayalite, and substituting a new data set for enstatite will help to improve the accuracy of PHOENIX models. Effective medium theory was found to not be a significant contributor to the calculations of the mean opacity.