Abstract
Determine the uncertainty relations between the orbital angular momentum \(\hat L = \left( {{{\hat L}_x},{{\hat L}_y},{{\hat L}_z}} \right)\) and the components of the position and of the momentum operators \(\hat r = \left( {\hat x,\hat y,\hat z} \right),\hat p = \left( {{{\hat p}_x},{{\hat p}_y},{{\hat p}_z}} \right)\). Then, find the operator \({\hat L_z}\) in spherical polar coordinates and explain why the operators \(\hat \phi\) (azimuthal angle) and \({\hat L_z}\) can be measured simultaneously. What are the functions of \(\hat \phi\) whose commutator with \({\hat L_z}\) has a physical sense?
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsAuthor information
Authors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Italia
About this chapter
Cite this chapter
Cini, M., Fucito, F., Sbragaglia, M. (2012). Angular Momentum and Spin. In: Solved Problems in Quantum and Statistical Mechanics. UNITEXT(). Springer, Milano. https://doi.org/10.1007/978-88-470-2315-4_3
Download citation
DOI: https://doi.org/10.1007/978-88-470-2315-4_3
Publisher Name: Springer, Milano
Print ISBN: 978-88-470-2314-7
Online ISBN: 978-88-470-2315-4
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)