Next Article in Journal
Recognition of Traveling Surges in HVDC with Wavelet Entropy
Next Article in Special Issue
About the Concept of Quantum Chaos
Previous Article in Journal
En-LDA: An Novel Approach to Automatic Bug Report Assignment with Entropy Optimized Latent Dirichlet Allocation
Previous Article in Special Issue
Using Measured Values in Bell’s Inequalities Entails at Least One Hypothesis in Addition to Local Realism
Article Menu
Issue 5 (May) cover image

Export Article

Open AccessArticle
Entropy 2017, 19(5), 186; doi:10.3390/e19050186

A Quantum Description of the Stern–Gerlach Experiment

1
Division of Physical Chemistry, Chemical Center, P.O. Box 124, University of Lund, SE 22100 Lund, Sweden
2
Department of Chemistry, Biological and Theoretical Chemistry, Umeå University, 901 87 Umeå, Sweden
*
Authors to whom correspondence should be addressed.
Academic Editors: Mariela Portesi, Alejandro Hnilo and Federico Holik
Received: 16 February 2017 / Revised: 19 April 2017 / Accepted: 20 April 2017 / Published: 25 April 2017
(This article belongs to the Special Issue Foundations of Quantum Mechanics)
View Full-Text   |   Download PDF [1002 KB, uploaded 25 April 2017]   |  

Abstract

A detailed analysis of the classic Stern–Gerlach experiment is presented. An analytical simple solution is presented for the quantum description of the translational and spin dynamics of a silver atom in a magnetic field with a gradient along a single z-direction. This description is then used to obtain an approximate quantum description of the more realistic case with a magnetic field gradient also in a second y-direction. An explicit relation is derived for how an initial off center deviation in the y-direction affects the final result observed at the detector. This shows that the “mouth shape” pattern at the detector observed in the original Stern–Gerlach experiment is a generic consequence of the gradient in the y-direction. This is followed by a discussion of the spin dynamics during the entry of the silver atom into the magnet. An analytical relation is derived for a simplified case of a field only along the z-direction. A central question for the conceptual understanding of the Stern–Gerlach experiment has been how an initially unpolarized spin ends up in a polarized state at the detector. It is argued that this can be understood with the use of the adiabatic approximation. When the atoms first experience the magnetic field outside the magnet, there is in general a change in the spin state, which transforms from a degenerate eigenstate in the absence of a field into one of two possible non-degenerate states in the field. If the direction of the field changes during the passage through the device, there is a corresponding adiabatic change of the spin state. It is shown that an application of the adiabatic approximation in this way is consistent with the previously derived exact relations. View Full-Text
Keywords: Stern–Gerlach experiment; quantum description and interpretation; adiabatic approximation; spin dynamics; spin density matrix, relaxation Stern–Gerlach experiment; quantum description and interpretation; adiabatic approximation; spin dynamics; spin density matrix, relaxation
Figures

Figure 1

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

Scifeed alert for new publications

Never miss any articles matching your research from any publisher
  • Get alerts for new papers matching your research
  • Find out the new papers from selected authors
  • Updated daily for 49'000+ journals and 6000+ publishers
  • Define your Scifeed now

SciFeed Share & Cite This Article

MDPI and ACS Style

Wennerström, H.; Westlund, P.-O. A Quantum Description of the Stern–Gerlach Experiment. Entropy 2017, 19, 186.

Show more citation formats Show less citations formats

Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Related Articles

Article Metrics

Article Access Statistics

1

Comments

[Return to top]
Entropy EISSN 1099-4300 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top