An Algebraic Approach to Quantum Systems Using Finite Group Representation

• Main Author: Choi, Brian Jongwon
• Format: Others
• Language: English
• Published: Boston College 2014
• Subjects: Mathematics; Physics; Representation; Quantum
• Online Access: http://hdl.handle.net/2345/3888

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.