Abstract
In this chapter, we show how uncertainty relations arise naturally from quantum theory for position and momentum, time and energy, and so on. We explore the meaning of these relations and apply them to the quantum mechanical description of the pendulum. We then use our new-found knowledge of the pendulum to construct Schrödinger cat-like states in opto-mechanical systems. Finally, we show how we can use entanglement to enhance the precision of measurements.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
W. Heisenberg, Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik, Zeitschrift für Physik, 43 172, 1927.
- 2.
H. P. Robertson, The Uncertainty Principle, Phys. Rev. 34 163, 1929.
- 3.
A. Einstein, B. Podolsky, and N. Rosen, Can Quantum-Mechanical Description of Physical Reality be Considered Complete?, Phys. Rev. 47 777, 1935.
- 4.
J. S. Bell, On the Einstein Podolsky Rosen Paradox, Physics 1 195, 1964.
- 5.
E. Schrödinger, Die gegenwärtige Situation in der Quantenmechanik, Naturwissenschaften 23 807, 1935.
- 6.
S. Gerlich et al., Quantum interference of large organic molecules, Nature Communications 2 263, 2011.
- 7.
M. Holland and K. Burnett, Interferometric detection of optical phase shifts at the Heisenberg limit, Phys. Rev. Lett. 71 1355, 1993.
Author information
Authors and Affiliations
Corresponding author
9.1 Electronic supplementary material
Below is the link to the electronic supplementary material.
Rights and permissions
Copyright information
© 2023 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this chapter
Cite this chapter
Kok, P. (2023). Quantum Uncertainty. In: A First Introduction to Quantum Physics. Undergraduate Lecture Notes in Physics. Springer, Cham. https://doi.org/10.1007/978-3-031-16165-0_9
Download citation
DOI: https://doi.org/10.1007/978-3-031-16165-0_9
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-031-16164-3
Online ISBN: 978-3-031-16165-0
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)