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- All Subjects: Quantum Mechanics
- All Subjects: optics
- Creators: Department of Physics
This work has been carried out under the guidance of the author’s thesis advisor, Professor Tingyong Chen.
This thesis attempts to explain Everettian quantum mechanics from the ground up, such that those with little to no experience in quantum physics can understand it. First, we introduce the history of quantum theory, and some concepts that make up the framework of quantum physics. Through these concepts, we reveal why interpretations are necessary to map the quantum world onto our classical world. We then introduce the Copenhagen interpretation, and how many-worlds differs from it. From there, we dive into the concepts of entanglement and decoherence, explaining how worlds branch in an Everettian universe, and how an Everettian universe can appear as our classical observed world. From there, we attempt to answer common questions about many-worlds and discuss whether there are philosophical ramifications to believing such a theory. Finally, we look at whether the many-worlds interpretation can be proven, and why one might choose to believe it.
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.
As the search for life in our universe grows, it is important to not only locate planets outside of our solar system, but also to work towards the ability to understand and characterize their nature. Many current research endeavors focus on the discovery of exoplanets throughout the surrounding universe; however, we still know very little about the characteristics of these exoplanets themselves, particularly their atmospheres. Observatories, such as the Hubble Space Telescope and the Spitzer Space Telescope, have made some of the first observations which revealed information about the atmospheres of exoplanets but have yet to acquire complete and detailed characterizations of exoplanet atmospheres. The EXoplanet Climate Infrared TElescope (EXCITE) is a mission specifically designed to target key information about the atmospheres of exoplanets - including the global and spatially resolved energy budget, chemical bulk-compositions, vertical temperature profiles and circulation patterns across the surface, energy distribution efficiency as a function of equilibrium temperatures, and cloud formation and distribution - in order to generate dynamic and detailed atmospheric characterizations. EXCITE will use phase-resolved transit spectroscopy in the 1-4 micron wavelength range to accomplish these science goals, so it is important that the EXCITE spectrograph system is designed and tested to meet these observational requirements. For my thesis, I present my research on the EXCITE mission science goals and the design of the EXCITE spectrograph system to meet these goals, along with the work I have done in the beginning stages of testing the EXCITE spectrograph system in the lab. The primary result of my research work is the preparation of a simple optics setup in the lab to prepare a laser light source for use in the EXCITE spectrograph system - comparable to the preparation of incoming light by the EXCITE telescope system - which successfully yields an F# = 12.9 and a spot size of s = 39 ± 7 microns. These results meet the expectations of the system and convey appropriate preparation of a light source to begin the assembly and testing of the EXCITE spectrograph optics in the lab.
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.
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.