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A quantum description of the Stern-Gerlach experiment

Wennerström, Håkan LU and Westlund, Per-Olof (2017) In Entropy 19(5).
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 offcenter 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... (More)

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 offcenter 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 understoodwith 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.

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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Adiabatic approximation, Quantumdescription and interpretation, Spin density matrix, relaxation, Spin dynamics, Stern-Gerlach experiment
in
Entropy
volume
19
issue
5
publisher
Multidisciplinary Digital Publishing Institute (MDPI)
external identifiers
  • scopus:85019197016
  • wos:000404453700005
DOI
10.3390/e19050186
language
English
LU publication?
yes
id
d6ec2e1d-46ac-4e78-8c55-882f3b519b52
date added to LUP
2017-05-31 11:06:20
date last changed
2018-05-13 04:31:55
@article{d6ec2e1d-46ac-4e78-8c55-882f3b519b52,
  abstract     = {<p>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 offcenter 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 understoodwith 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.</p>},
  articleno    = {186},
  author       = {Wennerström, Håkan and Westlund, Per-Olof},
  keyword      = {Adiabatic approximation,Quantumdescription and interpretation,Spin density matrix, relaxation,Spin dynamics,Stern-Gerlach experiment},
  language     = {eng},
  month        = {05},
  number       = {5},
  publisher    = {Multidisciplinary Digital Publishing Institute (MDPI)},
  series       = {Entropy},
  title        = {A quantum description of the Stern-Gerlach experiment},
  url          = {http://dx.doi.org/10.3390/e19050186},
  volume       = {19},
  year         = {2017},
}