The purpose of this paper is to provide an analysis of entanglement and the particular problems it poses for some physicists. In addition to looking at the history of entanglement and non-locality, this paper will use the Bell Test as a means for demonstrating how entanglement works, which measures the behavior of electrons whose combined internal angular momentum is zero. This paper will go over Dr. Bell's famous inequality, which shows why the process of entanglement cannot be explained by traditional means of local processes. Entanglement will be viewed initially through the Copenhagen Interpretation, but this paper will also look at two particular models of quantum mechanics, de-Broglie Bohm theory and Everett's Many-Worlds Interpretation, and observe how they explain the behavior of spin and entangled particles compared to the Copenhagen Interpretation.

In thesis we will build up our operator theory for finite and infinite dimensional systems. We then prove that Heisenberg and Schrodinger representations are equivalent for systems with finite degrees of freedom. We will then make a case to switch to a C*-algebra formulation of quantum mechanics as we will prove that the Schrodinger and Heisenberg pictures become inadequate to full describe systems with infinitely many degrees of freedom because of inequivalent representations. This becomes important as we shift from single particle systems to quantum field theory, statistical mechanics, and many other areas of study. The goal of this thesis is to introduce these mathematical topics rigorously and prove that they are necessary for further study in particle physics.

Plant-made virus-like particles (VLPs), composed of HIV-1 Gag and deconstructed gp41 proteins, have been shown to be safe and immunogenic in mice. Here, we report the successful production of HIV-1 Gag/dgp41 VLPs in Nicotiana benthamiana, using an enhanced geminivirus-based expression vector. This novel vector results in unique expression kinetics, with peak protein accumulation and minimal necrosis achieved on day 4 post-infiltration. In comparing various purification strategies, it was determined that a 20% ammonium sulfate precipitation is an effective and efficient method for removing plant proteins and purifying the recombinant VLPs of interest. If further purification is required, this may be achieved through ultracentrifugation. VLPs are a useful platform for a variety of biomedical applications and developing the technology to efficiently produce VLPs in the plant expression system is of critical importance.

This is a primer on the mathematic foundation of quantum mechanics. It seeks to introduce the topic in such a way that it is useful to both mathematicians and physicists by providing an extended example of abstract math concepts to work through and by going more in-depth in the math formalism than would normally be covered in a quantum mechanics class. The thesis begins by investigating functional analysis topics such as the Hilbert space and operators acting on them. Then it goes on to the postulates of quantum mechanics which extends the math formalism covered before to physics and works as the foundation for the rest of quantum mechanics.