On the uncertainty relations for an electron in a constant magnetic field

2012/07/30 by Francisco M. Fernández, Fernández, Francisco M.
Decision Sciences · Physics and Astronomy · #FOS: Physical sciences #Quantum Mechanics and Applications #Quantum Physics (quant-ph) #Radioactive Decay and Measurement Techniques #Scientific Measurement and Uncertainty Evaluation #quant-ph

paper · pdf · doi:10.48550/arxiv.1207.7069

arxiv created 2012/07/30 · openalex publication_date 2012/07/30 · arxiv updated 2012/08/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We discuss the uncertainty relation for the azimuthal angle ϕ and the z-component of the angular momentum L_z. To this end we derive the uncertainty relation for an arbitrary pair of observables and discuss the conditions for its validity. By means of a simple parameter-dependent state we illustrate the well known fact that the standard uncertainty relation for the coordinate and its conjugate momentum does not apply the pair of observables ϕ-L_z. This analysis is motivated by a discussion of the motion of an electron in a constant magnetic field appeared recently in this journal (Eur. J. Phys. 33 (2012) 1147) where the author assumed the validity of the standard uncertainty relation for the pair ϕ-L_z.

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