Comparing the Schr\"odinger and Dirac Descriptions of an Electron in a Uniform Magnetic Field
Abstract
In this article we present a detailed description of an electron in a uniform magnetic field evolving under the Schr\"odinger equation using ladder operators. Based on this analysis, we describe the same physical system using the Dirac equation, known from relativistic quantum mechanics. The main differences between these two quantum mechanical approaches are discussed and we observe specifically how the relativistic phenomena modify the description of this particular quantum system.
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