# The Path Integral Formulation of Quantum Mechanics

### From FSUPhysicsWiki

In this chapter, we discuss a formulation of quantum mechanics developed by Richard Feynman that describes a system in terms of propagators that "evolve" a state into another state. These propagators are given by a "sum over histories" of a phase factor that is, in turn, given by the action of the system over the relevant time interval. This "sum over histories" is expressed in terms of a path integral. This is a quantum mechanical generalization of the action principle of classical mechanics, since this integral will favor "histories" that do not deviate significantly from the classical trajectory of the system.

We will briefly introduce the path integral formulation, then show how to evaluate this integral for two special cases, namely for a free particle and for the harmonic oscillator.