2013 Student Research Conference:

26th Annual Student Research Conference

26th Annual Student Research Conference

**Interpreting the Wigner Function as a Probability Current Density**

Dipesh Niraula

Prof. Taner Edis, Faculty Mentor

All formulations of Quantum mechanics predict probabilities and averages. The phase space formulation of quantum mechanics does this through Wigner functions, which are quasi-probability distributions which are like probability distributions except that they can have negative values. We try to understand Wigner functions as a probability current density, since current density can have negative values. We interpret negative values of the Wigner function as a tendency of a particle to go backward in time. To account for travel backward in time, we introduce a probability density ρ(x,p,t; τ), with τ as an extra parameter describing the particle trajectory in extended phase space. We then seek a partial differential equation that describes the τ-evolution of ρ. From this equation and the continuity equation expressing the conservation of probability, we can then find the time component of the probability current. We propose that a Wigner function might be this current component, integrated over τ.

**Keywords:** Wigner function, time travel

**Topic(s):**Physics

**Presentation Type:** Oral Paper

**Session:** 305-2

**Location:** MG 1096

**Time:** 1:15