| Summary: | Thesis advisor: Dubi Kelmer === Undergraduate physics emphasizes the Schrödinger's analytic approach in solving and understanding quantum systems. Although briefly mentioned, group-theoretic approach is not emphasized, at least in terms of mathematical rigour. I attempt to kill the two rabbits - rigour and application. Part I develops the necessary formal theory of representation of finite group. In part II: Application, I primarily focus on the behaviour of an electron in various potentials where the spherical symmetry of an atom is broken into finite symmetry where I can readily apply the machineries that I have developed in part I. Basic notions of group theory, linear algebra and quantum mechanics are assumed. === Thesis (BS) — Boston College, 2014. === Submitted to: Boston College. College of Arts and Sciences. === Discipline: Mathematics Honors Program. === Discipline: College Honors Program. === Discipline: Mathematics.
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