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

• URL: http://arxiv.org/abs/2606.13290v1
• Date: Thu, 11 Jun 2026 12:46:41 GMT
• Title: Understanding quantum behaviors of an electron in a uniform magnetic field alternatively
• Abstract summary: For states with a negative angular quantum number, the total probability current vanishes.<n>We show that the vanishing total current results from an exact cancellation between two regions.<n>The negative quantum number manifests in the strength of the inner counter-rotation, while the net kinetic angular momentum remains positive.
• Score: 3.284878354988896
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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