Understanding quantum behaviors of an electron in a uniform magnetic field alternatively

Abstract:Quantum mechanically, an electron moving in a uniform magnetic field forms Landau levels. A curious feature is that for states with a negative angular quantum number, the total probability current vanishes, which appears to contradict the classical picture of cyclotron motion. While a geometric interpretation based on classical orbits exists, alternative interpretations remain of interest. In this paper, we examine the probability current density and identify a critical radius that naturally partitions the plane into an inner clockwise-flow region and an outer counterclockwise-flow region. We show that the vanishing total current results from an exact cancellation between these two regions. Furthermore, by defining a partitioned kinetic angular momentum with respect to the critical radius, we reveal an intrinsic competitive structure: the electron simultaneously carries two opposing rotational components. The negative quantum number manifests in the strength of the inner counter-rotation, while the net kinetic angular momentum remains positive. This bidirectional flow picture also provides a dynamical interpretation of the infinite degeneracy of Landau levels.

Mesoscale and Nanoscale Physics (cond-mat.mes-hall); Quantum Physics (quant-ph)

arXiv:2606.13290 [cond-mat.mes-hall]

(or arXiv:2606.13290v1 [cond-mat.mes-hall] for this version)

https://doi.org/10.48550/arXiv.2606.13290 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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