Energy of a finite three-dimensional electron gas of spinless electrons

Ciftja, Orion

doi:10.1016/j.jpcs.2019.109135

Cited by 4 publications

(1 citation statement)

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“…When thinking of real materials such as conductors, classically, the Lorentz force acting on quasi-free electrons bends their trajectories. This affects transport properties of metals and semiconductors [4][5][6]. One important phenomenon observed under these conditions is the appearance of an electric field perpendicular to the direction of the current flow known as the classical Hall effect [7].…”

Section: Introductionmentioning

confidence: 99%

Detailed solution of the problem of Landau states in a symmetric gauge

Ciftja

2020

Eur. J. Phys.

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Understanding the quantum problem of a free charged particle undergoing two-dimensional motion in a perpendicular uniform, constant magnetic field is necessary to the comprehension of some very important phenomena in physics. In particular, a grasp of the nature of the Landau states in a symmetric gauge is crucial to explain the underlying principles of quantum Hall effects. In this work we provide a step-by-step solution of this quantum problem in a pedagogical fashion that is easy to follow by an audience of undergraduate students and prospective physics teachers. This approach should enable undergraduate students to comprehend all the technical mathematical details involved in the process. Such details are routinely missing from mainstream quantum mechanics textbooks. In particular, this study allows a broad audience of students and teachers to gradually absorb knowledge not only on basic principles of quantum mechanics, but also on various special mathematical functions that are encountered in the process.

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