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Physical Interpretation of Relativity Theory Proceedings of International Meeting

Movement of a relativistic particle in a spherical potential box

Николай Ильич Юрасов, I.I. Yurasova

Published Dec 1, 2015• 0 citations
Publisher

Abstract

The problem of a relativistic particle in a spherical potential box with impenetrable walls has investigated.The power spectrum has found.Comparison with the specified characteristics for a similar not relativistic problem has executed.Essential distinctions have revealed.Possibilities of application of the solved problem in astrophysics are considered.

DOI
10.18698/2309-7604-2015-1-559-565

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The problem of a relativistic particle in a spherical potential box with impenetrable walls has investigated.The power spectrum has found.Comparison with the specified characteristics for a similar not relativistic problem has executed.Essential distinctions have revealed.Possibilities of application of the solved problem in astrophysics are considered.
Abstract The problem of a particle in a box is probably the simplest problem in quantum mechanics which allows for significant insight into the nature of quantum systems and thus is a cornerstone in the teaching of quantum mechanics. In relativistic quantum mechanics this problem allows also to highlight the implications of special relativity for quantum physics, namely the effect that spin has on the quantised energy spectra. To illustrate this point, we solve the problem of a spin zero relativistic particle in a one- and three-dimensional box using the Klein–Gordon equation in the Feshbach–Villars formalism. We compare the solutions and the energy spectra obtained with the corresponding ones from the Dirac equation for a spin one-half relativistic particle. We note the similarities and differences, in particular the spin effects in the relativistic energy spectrum. As expected, the non-relativistic limit is the same for both kinds of particles, since, for a particle in a box, the spin contribution to the energy is a relativistic effect.
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.