Classical and quantum mechanical motion in magnetic fields

We study the motion of a particle in a particular magnetic field configuration both classically and quantum mechanically. For flux-free radially symmetric magnetic fields defined on circular regions, we establish that particle escape speeds depend, classically, on a gauge-fixed magnetic vector poten...

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Veröffentlicht in:American journal of physics 2016-04, Vol.84 (4), p.263-269
Hauptverfasser: Franklin, J., Cole Newton, K.
Format: Artikel
Sprache:eng
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Zusammenfassung:We study the motion of a particle in a particular magnetic field configuration both classically and quantum mechanically. For flux-free radially symmetric magnetic fields defined on circular regions, we establish that particle escape speeds depend, classically, on a gauge-fixed magnetic vector potential, and we demonstrate some trajectories associated with this special type of magnetic field. Then we show that some of the geometric features of the classical trajectory (perpendicular exit from the field region, trapped and escape behavior) are reproduced quantum mechanically, using a numerical method that extends the norm-preserving Crank-Nicolson method to problems involving magnetic fields. While there are similarities between the classical trajectory and the position expectation value of the quantum-mechanical solution, there are also differences, and we demonstrate some of these.
ISSN:0002-9505
1943-2909
DOI:10.1119/1.4941571