2010 Student Research Conference:

23rd Annual Student Research Conference

23rd Annual Student Research Conference

**Expanding Action Minimization to the Quantum Case**

Joseph A. Palmer

Dr. Taner Edis, Faculty Mentor

In classical mechanics an object follows the path of least action when moving between two points. A natural extension of this picture is to consider a quantum particle that does not follow a deterministic path, where the classical trajectory of least action is only the path of highest probability. The particle state would be given by an evolving pseudo-probability distribution in phase space. We generalize from trajectories in phase space to including those paths where a particle can move backwards in time, anticipating that the path of least action would always be future pointing. Actually some of the family of seemingly classically allowed paths travel backwards in time, and we explore this result. The intuitive solution for probability of a path, exp(-S), with S as the classical action, is not suited for this because it does not provide normalizable probability distributions, thus we explore alternate forms of the classical action.

**Keywords:** Quantum Mechanincs, Action Minimization, Phase Space, Arrow of Time, Pseudo-probability distribution

**Topic(s):**Physics

Mathematics

**Presentation Type:** Oral Paper

**Session:** 3-2

**Location:** MG 1096

**Time:** 8:15