2015 Student Research Conference:

28th Annual Student Research Conference

28th Annual Student Research Conference

**Quantum Mechanics in Phase Space: Wigner Functions as Derived from Currents**

Destry A. Newton

Prof. Taner Edis, Faculty Mentor

In the phase space formalism of quantum mechanics, a quantum state is represented by a Wigner function. Wigner functions are real valued, normalized functions of position, momentum and time, similar to 2n-dimensional probability distributions. Unlike probability distributions though, Wigner functions can have regions in phase space where they are negative. We aim to interpret these negative regions as back-flow in time. We examine the quantum simple harmonic oscillator. Starting from a positive-definite probability density that is parameterized along the path of the particle, we determine the probability current density of the particle and hope to show that by integrating out the path parameter from the current density a Wigner function is recovered. To approach this problem, we worked with differential equations that govern how a probability density evolves along the particles path and with the continuity equation, to relate the evolution of a probability density to corresponding probability density currents.

**Keywords:** quantum mechanics, phase space, Wigner functions, differential equations

**Topic(s):**Physics

Mathematics

**Presentation Type:** Oral Paper

**Session:** 310-4

**Location:** MG 1096

**Time:** 1:45