Abstract
Abstract In this article we present a detailed description, using ladder operators, of an electron in a uniform magnetic field evolving under the Schrodinger equation. We go on to describe the same physical system in terms of relativistic quantum mechanics using the Dirac equation and to compare the two models in detail. 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 by isolating effects which only exist in the relativistic model.
Highlights
In this article we present the detailed calculations required for a didactic comparison between the dynamics of the Schrödinger and Dirac equations for an electron in a uniform magnetic field
This is done in order to juxtapose these two quantum mechanical descriptions of the same system as a pedagogic tool
Our analysis provides an invaluable resource to instructors, who could make use of this example, either for an advanced undergraduate quantum mechanics course or for a beginning graduate course
Summary
In this article we present the detailed calculations required for a didactic comparison between the dynamics of the Schrödinger and Dirac equations for an electron in a uniform magnetic field This is done in order to juxtapose these two quantum mechanical descriptions of the same system as a pedagogic tool. For specific examples see both electron vortex beams [7,8,9] and the interaction of solid state materials with magnetism [10,11,12,13,14] (known as the integer Quantum Hall effect) This specific physical system shows a certain isomorphism to quantum optics, demonstrating a narrow relation to describe the Gaussian beam profile of electromagnetic radiation, leading to orthogonal states known as Orbital Angular Momentum of light [15].
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