Quantum Mechanics A Mathematical Introduction

In this chapter, we will introduce the , which is a formulation of quantum mechanics equivalent to the Schrödinger equation, but has a profoundly distinct interpretation. Further, the path integral is very easily extended to incorporate special relativity, which is very challenging and inconvenient within the context of the Schrödinger equation. So, what is the idea of this path integral? Our goal will be to calculate the amplitude for a quantum mechanical particle that starts at position xi at time t = 0 and ends at position xf at some later time t=T>0. In some sense, this question is analogous to what you ask in an introduction to kinematics in introductory physics; however, its analysis in quantum mechanics will prove to be a bit more complicated than that in the first week of your first course in physics.