Honors Directed Study Abstract - PS 303 Modern Physics Honors Projects

1.1 Project 1\nThe objective of the first project was to explore special relativity by determining the center- of-mass energies of both collider particle accelerators and fixed target particle accelerators. Then, the center-of-mass energies were plotted as a function of time, or rather the year the accelerator was first operated. For each accelerator, the beam, target, and accomplishments from the experiments done with the accelerator were identied. In addition, it was noted if the accelerator was still in operation. These were then plotted in MATLAB, and the center-of-mass energies for both types of accelerator were compared.\n1.2 Project 2\nThe objective of the second project was to explore quantum mechanics through the solutions to the quantum harmonic oscillator for the principle quantum number n. This was done by finding the probability densities and comparing to the actual probability density of a classical harmonic oscillator in order to verify the Correspondence Principle, which states that for high values of n, the system should resemble that of the classical model rather than the non-intuitive system at lower n values. The classical model follows a 1 2kx2 curve, which was exhibited in the n=50 and partially in the n=10, but differed considerably from the n=2 state.