Abstract
State vectors and other matrices are introduced. We also define projection matrices for the interpretation of experiments and density matrices for the description of mixed states. Also, Heisenberg’s famous uncertainty relation is derived and interpreted.
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 subscriptionsNotes
- 1.
Otto Stern, 1888–1969, German physicist, Nobel Prize 1943.
- 2.
Walther Gerlach, 1889–1979, German physicist.
- 3.
A complete set of eigenvectors is a set of eigenvectors so that every vector is a linear combination of the eigenvectors.
- 4.
The same holds if we only have incomplete information on the system, for example if the particle number is very large and when we can only make probability statements.
- 5.
With \(\left\langle [\varvec{A },\varvec{B }]\right\rangle {\mathop {=}\limits ^{\mathrm{def}}}\varvec{\xi }^\dagger [\varvec{A },\varvec{B }]\,\varvec{\xi }\).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG
About this chapter
Cite this chapter
Ludyk, G. (2018). Observables and Uncertainty Relations. In: Quantum Mechanics in Matrix Form. Springer, Cham. https://doi.org/10.1007/978-3-319-26366-3_4
Download citation
DOI: https://doi.org/10.1007/978-3-319-26366-3_4
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-26364-9
Online ISBN: 978-3-319-26366-3
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)