An Algebraic Approach to Quantum Systems Using Finite Group Representation

Abstract

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.