Phase-Space Position-Momentum Correlation and Potentials

Solutions to the radial Schr¨odinger equation of a particle in a quantum corral are used to probe how the statistical correlation between the position, and The momentum of the particle depends on the effective potential. The analysis is done via the Wigner function and its Shannon entropy. We show by comparison to the particle-in-a-box model that the attractive potential increases the magnitude of the correlation, while a repulsive potential decreases the magnitude of this correlation. Varying the magnitude of the repulsive potential yields that the correlation decreases with a stronger repulsive potential.