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WKB analysis of relativistic Stern-Gerlach measurements

AuthorsPalmer, Matthew C.; Takahashi, M.; Westman, H.F.
Issue Date2013
PublisherAcademic Press
CitationAnnals of Physics 336: 505- 516 (2013)
AbstractSpin is an important quantum degree of freedom in relativistic quantum information theory. This paper provides a first-principles derivation of the observable corresponding to a Stern-Gerlach measurement with relativistic particle velocity. The specific mathematical form of the Stern-Gerlach operator is established using the transformation properties of the electromagnetic field. To confirm that this is indeed the correct operator we provide a detailed analysis of the Stern-Gerlach measurement process. We do this by applying a WKB approximation to the minimally coupled Dirac equation describing an interaction between a massive fermion and an electromagnetic field. Making use of the superposition principle we show that the +1 and -1 spin eigenstates of the proposed spin operator are split into separate packets due to the inhomogeneity of the Stern-Gerlach magnetic field. The operator we obtain is dependent on the momentum between particle and Stern-Gerlach apparatus, and is mathematically distinct from two other commonly used operators. The consequences for quantum tomography are consider. © 2013 Elsevier Inc.
Identifiersdoi: 10.1016/j.aop.2013.05.017
issn: 0003-4916
Appears in Collections:(CFMAC-IFF) Artículos
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