Solutions of the Dirac equation in one-dimensional variable width potential well

• URL: http://arxiv.org/abs/2107.05361v5
• Date: Wed, 12 Feb 2025 13:27:52 GMT
• Title: Solutions of the Dirac equation in one-dimensional variable width potential well
• Authors: Qiuyu Shan,
• Abstract summary: When the width of a potential well changes over time, the velocity of particles within the well also changes. For quantum systems, such dynamics should be described by the Schr"odinger, Klein-Gordon, and Dirac equations. Previous studies have solved the Schr"odinger and Klein-Gordon equations under these conditions, but no research has addressed the Dirac equation for spin-$frac12$ particles like electrons.
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• Abstract: The Fermi acceleration mechanism is a significant source of cosmic rays. When the width of a potential well changes over time, the velocity of particles within the well also changes. For quantum systems, such dynamics should be described by the Schr\"odinger, Klein-Gordon, and Dirac equations. Previous studies have solved the Schr\"odinger and Klein-Gordon equations under these conditions, but no research has addressed the Dirac equation for spin-$\frac{1}{2}$ particles like electrons. This paper investigates the solutions of the Dirac equation in a dynamically varying potential well.

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