WKB analysis of relativistic Stern–Gerlach measurements
- School of Physics, The University of Sydney, Sydney, NSW 2006 (Australia)
Spin 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 considered. -- Highlights: •Derivation of the spin observable for a relativistic Stern–Gerlach measurement. •Relativistic model of spin measurement using WKB approximation of Dirac equation. •The derived spin operator is distinct from two other commonly used operators. •Consequences for quantum tomography are considered.
- OSTI ID:
- 22220790
- Journal Information:
- Annals of Physics (New York), Vol. 336; Other Information: Copyright (c) 2013 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA); ISSN 0003-4916
- Country of Publication:
- United States
- Language:
- English
Similar Records
Quantum mechanical description of Stern-Gerlach experiments
Stern-Gerlach Effect for Electron Beams