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Proceedings of the Indiana Academy of Science

A simple method for obtaining the solutions of Dirac's equation for a free particle in spherical coordinates

Jeff Carlson

Published Jan 1, 1939• 0 citations
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We consider a Dirac particle in a spherical box with a time-dependent radius. Analytical and numerical solutions of the time-dependent Dirac equation with time-dependent boundary (Dirichlet) conditions are obtained. Using the obtained solutions, physically observable characteristics of the dynamical confinement, such as the average kinetic energy (as a function of time) and average quantum force acting on the particle by the moving wall, are calculated. The trembling motion is analysed by computing the average coordinate of the Dirac particle as a function of time. The absence of the geometric phase is shown by direct calculation.