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Non-Relativistic Limit of the Dirac Equation

Published by International Journal of Quantum Foundations on June 26, 2016

Volume 2, Issue 3, pages 109-120

Muhammad Adeel Ajaib [Show Biography]

Dr. Muhammad Adeel Ajaib was born in Dubai, U.A.E, in 1983. He received his PhD in theoretical particle physics from the University of Delaware in 2014. In research, his topics of interests include supersymmetry, fundamental physics and overlapping ideas of various subfields in physics. His achievements include proposing a fundamental form of the Schrodinger equation. He also showed how a well known interaction in spintronics, called the Rashba interaction, can be obtained from a Lorentz violating operator in the Standard Model Extension. After completing his PhD, he worked at Ursinus college as visiting assintant professor for one year and is currently a lecturer in physics at California Polytechnic State University, San Luis Obispo.

We show that the first order form of the Schrödinger equation proposed in [1] can be obtained from the Dirac equation in the non-relativistic limit. We also show that the Pauli Hamiltonian is obtained from this equation by requiring local gauge invariance. In addition, we study the problem of a spin up particle incident on a finite potential barrier and show that the known quantum mechanical results are obtained. Finally, we consider the symmetric potential well and show that the quantum mechanical expression for the quantized energy levels of a particle is obtained with periodic boundary conditions. Based on these conclusions, we propose that the equation introduced in [1] is the non-relativistic limit of the Dirac equation and more appropriately describes spin 1/2 particles in the non-relativistic limit.

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Posted in Volume 2, Issue 3, July 2016 Tagged Original Paper

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