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arXiv:quant-ph/0108069 · Physical Review A

Quantum anticentrifugal force

M. A. Cirone, Kazimierz Rza̧żewski, Wolfgang P. Schleich, F. Straub, JOHN ARCHIBALD WHEELER

Published Dec 21, 2001• 39 citations
arXivHTMLPDF

Abstract

In a two-dimensional world, a free quantum particle of vanishing angular momentum experiences an attractive force. This force originates from a modification of the classical centrifugal force due to the wave nature of the particle. For positive energies the quantum anticentrifugal force manifests itself in a bunching of the nodes of the energy wave functions towards the origin. For negative energies this force is sufficient to create a bound state in a two-dimensional \ensuremath{\delta}-function potential. In a counterintuitive way, the attractive force pushes the particle away from the location of the \ensuremath{\delta}-function potential. As a consequence, the particle is localized in a band-shaped domain around the origin.

DOI
10.1103/physreva.65.022101

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In a two-dimensional world, a free quantum particle of vanishing angular momentum experiences an attractive force. This force originates from a modification of the classical centrifugal force due to the wave nature of the particle. For positive energies the quantum anticentrifugal force manifests itself in a bunching of the nodes of the energy wave functions towards the origin. For negative energies this force is sufficient to create a bound state in a two-dimensional \ensuremath{\delta}-function potential. In a counterintuitive way, the attractive force pushes the particle away from the location of the \ensuremath{\delta}-function potential. As a consequence, the particle is localized in a band-shaped domain around the origin.
A quantum potential V (x, t) of δ-function type is introduced, to describe the motion of a particle. Quantum-mechanically, it is in a bound state (potential trap of Hojman and Asenjo [6]), though classically one seems to be free. The motion of the object takes place according to the Huygens-Fresnel principle. The new position of the object (wave front) plays the role of the secondary sources that maintain the propagation. We found that the de Broglie-Bohm quantum potential is the difference between the constant bound energy E = −mc 2 /2 from the stationary case and our potential V (x, t).