Abstract
We construct phase-space representations for a relativistic particle in both a constant and a time-dependent linear potential. We obtain explicit expressions for the Wigner distribution functions for these systems and find the correct nonrelativistic limit and free-particle limit for these functions. We derive the relativistic dynamical equation governing the time development of the Wigner distribution function and relativistic equation for the Wigner distribution function of stationary states and also calculate the amplitudes of transitions between energy states.
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This research is supported by the Science Development Foundation under the President of the Republic of Azerbaijan (Research Grant No. EIF-2012-2(6)-39/08/1).
Prepared from an English manuscript submitted by the author; for the Russian version, see Teoreticheskaya i Matematicheskaya Fizika, Vol. 188, No. 1, pp. 76–84, July, 2016.
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Nagiyev, S.M. Wigner function of a relativistic particle in a time-dependent linear potential. Theor Math Phys 188, 1030–1037 (2016). https://doi.org/10.1134/S0040577916070059
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DOI: https://doi.org/10.1134/S0040577916070059