Abstract
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.
Highlights
The position and momentum of a quantum particle are intimately related and correlated, since knowledge of one precludes knowledge of the other
Wigner functions and their Shannon entropies were calculated by numerical Fourier transform of: Wnk (r, p) =
The localization/delocalization in the Wigner function is studied by its Shannon entropy
Summary
The position and momentum of a quantum particle are intimately related and correlated, since knowledge of one precludes knowledge of the other. It is this correlation which gives rise to the Heisenberg uncertainty principle. In quantum mechanical formulism, the position operator does not commute with the momentum operator. The momentum space wavefunction is the Dirac-Fourier transform (FT) of the position space one: φ(p) = 1 ∫. This FT illustrates that each point in p-space is intertwined with every point in x-space, and vice versa. One introduces a phase-space distribution that is dependent on both x and p
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