Date of Award

Spring 5-20-2016

Author's School

College of Arts & Sciences

Author's Program

Mathematics

Degree Name

Bachelor of Arts (A.B.)

Restricted/Unrestricted

Unrestricted

Abstract

In this paper, we will explore some of the basic elements of the mathematical formulation of quantum mechanics. In the first section, I will list the motivations for introducing a probability model that is quite different from that of the classical probability theory, but still shares quite a few significant commonalities. Later in the paper, I will discuss the quantum probability theory in detail, while paying a brief attention to some of the axioms (by Birkhoff and von Neumann) that illustrate both the commonalities and differences between classical mechanics and quantum mechanics. This paper will end with a presentation of two theorems that form the core of quantum mechanics.

Mentor

Renato Feres, Xiang Tang