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Adiabatic motion of a neutral spinning particle in an inhomogeneous magnetic field

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Publication details

JournalPhysical Review A
DatePublished - Aug 1993
Issue number2
Number of pages16
Pages (from-to)924-940
Original languageEnglish


The motion of a neutral particle with a magnetic moment in an inhomogeneous magnetic field is considered. This situation, occurring, for example, in a Stern-Gerlach experiment, is investigated from classical and semiclassical points of view. It is assumed that the magnetic field is strong or slowly varying in space, i.e., that adiabatic conditions hold. To the classical model, a systematic Lie-transform perturbation technique is applied up to second order in the adiabatic-expansion parameter. The averaged classical Hamiltonian contains not only terms representing fictitious electric and magnetic fields but also an additional velocity-dependent potential. The Hamiltonian of the quantum-mechanical system is diagonalized by means of a systematic WKB analysis for coupled wave equations up to second order in the adiabaticity parameter, which is coupled to Planck’s constant. An exact term-by-term correspondence with the averaged classical Hamiltonian is established, thus confirming the relevance of the additional velocity-dependent second-order contribution.

Bibliographical note

© 1993 The American Physical Society. Reproduced in accordance with the publisher's self-archiving policy.

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