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Physics Letters A

Propagator for a harmonically bound charged particle in a constant magnetic field and with the vector potential of a solenoid

Bin Kang Cheng, ALVARO DE SOUZA DUTRA

Published Jul 1, 1987• 7 citations
Publisher
DOI
10.1016/0375-9601(87)90286-6

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The role of the Aharonov-Bohm effect is analyzed for the bound states of a charged particle in the superposition of two fields: A uniform magnetic field plus the vector potential of a solenoid. Exact solutions are given for a solenoid of zero size and the corrections due to finite size are discussed. It is shown that a series of new "betatron resonances" appear in the spectrum, dependent on the flux quantum number $f=\frac{e\ensuremath{\Phi}}{\mathrm{hc}}$. The fundamental betatron resonance remains narrow and unshifted for solenoid radii large enough to broaden and shift the cyclotron resonance.