2013 Student Research Conference:

26th Annual Student Research Conference

26th Annual Student Research Conference

**Quantum Mechanics in Phase Space:
Wigner's Function as a Current**

Robert A. Ashcraft

Dr. Taner Edis, Faculty Mentor

In the usual Hilbert Space formalism of quantum mechanics, wave functions, the fundamental mathematical objects, have no apparent physical interpretation. Since, given a wave function, quantum mechanics predicts probability distributions it is worthwhile to investigate if quantum mechanics can be formulated directly in terms of probabilities. There exists a phase space description of quantum mechanics in which the fundamental object is a "Wigner function", a function similar to a probability distribution except that it can be negative. Our work begins to explore if Wigner functions can be understood as currents for particles that travel backward as well as forward in time. This work included finding a general form, by using a central moment expansion, of the partial differential equation which would describe particle motion.

**Keywords:** Quantum Mechanics, Physics, Phase Space, Wigner function, currents

**Topic(s):**Physics

**Presentation Type:** Oral Paper

**Session:** 206-3

**Location:** MG 1096

**Time:** 10:00