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Open AccessArticle

A Quantum Description of the Stern–Gerlach Experiment

Division of Physical Chemistry, Chemical Center, P.O. Box 124, University of Lund, SE 22100 Lund, Sweden
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
Entropy 2017, 19(5), 186;
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)
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
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Wennerström, H.; Westlund, P.-O. A Quantum Description of the Stern–Gerlach Experiment. Entropy 2017, 19, 186.

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