English

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

Quantum Physics 2012-08-01 v1

Abstract

We discuss the uncertainty relation for the azimuthal angle ϕ\phi and the zz-component of the angular momentum LzL_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 ϕLz\phi-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. \textbf{33} (2012) 1147) where the author assumed the validity of the standard uncertainty relation for the pair ϕLz\phi-L_z.

Keywords

Cite

@article{arxiv.1207.7069,
  title  = {On the uncertainty relations for an electron in a constant magnetic field},
  author = {Francisco M. Fernández},
  journal= {arXiv preprint arXiv:1207.7069},
  year   = {2012}
}