{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,23]],"date-time":"2026-09-23T05:47:02Z","timestamp":1790142422239,"version":"4.0.1"},"reference-count":28,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2017,4,25]],"date-time":"2017-04-25T00:00:00Z","timestamp":1493078400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100004359","name":"Vetenskapsr\u00e5det","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100004359","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>A detailed analysis of the classic Stern\u2013Gerlach 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 \u201cmouth shape\u201d pattern at the detector observed in the original Stern\u2013Gerlach 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\u2013Gerlach 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.<\/jats:p>","DOI":"10.3390\/e19050186","type":"journal-article","created":{"date-parts":[[2017,4,25]],"date-time":"2017-04-25T13:21:12Z","timestamp":1493126472000},"page":"186","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["A Quantum Description of the Stern\u2013Gerlach Experiment"],"prefix":"10.3390","volume":"19","author":[{"given":"H\u00e5kan","family":"Wennerstr\u00f6m","sequence":"first","affiliation":[{"name":"Division of Physical Chemistry, Chemical Center, P.O. Box 124, University of Lund, SE 22100 Lund, Sweden"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Per-Olof","family":"Westlund","sequence":"additional","affiliation":[{"name":"Department of Chemistry, Biological and Theoretical Chemistry, Ume\u00e5 University, 901 87 Ume\u00e5, Sweden"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2017,4,25]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"349","DOI":"10.1007\/BF01326983","article-title":"Der experimentelle Nachweis der Richtungsquantelung im Magnetfeld","volume":"9","author":"Gerlach","year":"1922","journal-title":"Z. Phys."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"327","DOI":"10.1140\/epjh\/e2016-70053-2","article-title":"The Stern\u2013Gerlach Experiment Revisited","volume":"41","author":"Schmidt","year":"2016","journal-title":"Eur. Phys. J. 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