Investigation of an Equation with Logarithmic Coupling with Momentum in Dirac Equation
International Journal of High Energy Physics
Volume 7, Issue 2, December 2020, Pages: 32-36
Received: Jul. 7, 2020;
Accepted: Jul. 27, 2020;
Published: Aug. 10, 2020
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Mash-Huda Rahman Shipra, Department of Physics, Shahjalal University of Science and Technology, Sylhet, Bangladesh
Syed Badiuzzaman Faruque, Department of Physics, Shahjalal University of Science and Technology, Sylhet, Bangladesh
The free particle solutions of the relativistic Dirac equation are characterized by plane waves with infinite uncertainty in position. However, many practical implementations of the solutions require a wave packet configuration, which can be utilized to represent a localized Dirac particle. Unlike the traditional wave packet generation method by superposing multiple plane waves, this study of ours presents an alternative approach towards obtaining a wave packet solution of a free particle relativistic Dirac equation. In this paper, we present Dirac’s free particle equation with a modification in the generalized momentum. The modification is achieved by coupling the momentum with a spatially varying logarithmic function, and this alteration does not affect the relativistic dispersion relation of the particle. Moreover, a solution of this modified Dirac equation is provided as well, which has been calculated using a trial wave function. The wave function solution is carried out in one dimension, where it behaves as a wave packet for a given ratio of the envelope parameter to the reduced Planck's constant greater than unity, where the envelope parameter regulates the width of the wave packet. The solution, being subject to this constraint, represents a bound particle with spin and a continuous energy spectrum.
Mash-Huda Rahman Shipra,
Syed Badiuzzaman Faruque,
Investigation of an Equation with Logarithmic Coupling with Momentum in Dirac Equation, International Journal of High Energy Physics.
Vol. 7, No. 2,
2020, pp. 32-36.
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