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Large quantum probability backflow and the azimuthal angle–angular momentum uncertainty relation for an electron in a constant magnetic field

In this paper we demonstrate a surprising aspect of quantum mechanics that is accessible to an undergraduate student. We discuss probability backflow for an electron in a constant magnetic field. It is shown that even for a wavepacket composed entirely of states with negative angular momentum the effective angular momentum can take on positive values in some regions of space. This is also a demonstration of the azimuthal angle–angular momentum uncertainty relation. This example is chosen because the backflow motion persists indefinitely. However this work can easily be extended to other systems where the motion is notionally circular, such as the hydrogen atom.