Abstract
We summarize our results about the quantization of a charged particle motion without spin inside a flat box under a static electromagnetic field with Landau’s gauge for the magnetic field, where Fourier’s transformation was used to analyze the problem, to point out that there exists a wave function which is different to that one given by Landau with the same Landau’s levels. The quantization of the magnetic flux is deduced differently to previous one, and a new solution is presented for the case of symmetric gauge of the magnetic field, and having the same Landau’s levels.
Highlights
The work of Klitzing, Dora and Pepper [1] presented a breakthrough in experimental physics due to its success in measuring the Hall voltage of a twodimensional electron gas realized in a MOSFET
We summarize our results about the quantization of a charged particle motion without spin inside a flat box under a static electromagnetic field with Landau’s gauge for the magnetic field, where Fourier’s transformation was used to analyze the problem, to point out that there exists a wave function which is different to that one given by Landau with the same Landau’s levels
We have summarized our previous results about the quantization of a charged particle in a flat box and under constants magnetic and electric fields for several electromagnetic static cases using Landau’s gauge for the static magnetic field, and using Fourier transformation to solve the linear differential equations resulting from the Shrödinger’s equation
Summary
The work of Klitzing, Dora and Pepper [1] presented a breakthrough in experimental physics due to its success in measuring the Hall voltage of a twodimensional electron gas realized in a MOSFET. The important fact discovered in this experiment was that the Hall resistance is quantized, and Landau’s eigenvalues solution [2] (Landau’s levels) of a charged particle in a flat surface with magnetic field has become of great importance in trying to understand integer Hall effect [1] [3] [4] [5] [6], fractional Hall effect [6] [7] [8] [9], and topological insulators [10]-[14]. We summarize those results here and make a different approach to obtain the quantization of the magnetic flux or the density of states between two Landau’s levels. For the especial case where the charged particle is moving on the plane x-y under the same static transversal magnetic field but defined by the symmetric gauge, we present a new solution, which matches the characteristics mentioned in [18] and on this paper, we have the same Landau’s Levels as solution of the eigenvalue problem
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