dorsal/arxiv
View SchemaA complete analysis of the Stern-Gerlach experiment using Pauli spinors
| Authors | Michel Gondran, Alexandre Gondran |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0511276 |
| URL | https://arxiv.org/abs/quant-ph/0511276 |
Abstract
The Stern-Gerlach experiment is the fundamental experiment in order to exhibit the quantization of spin and understand the measurement problem in quantum mechanics. However, although the Stern-Gerlach experiment plays an essential role in the teaching of quantum mechanics, no complete analysis of this experiment using Pauli spinors is presented in the pedagogical literature. This paper presents such an analysis and develops implications for the theory of quantum measurement. We first propose an analytic expression of both the wave function and the probability density in the Stern-Gerlach experiment. Our explicit solution is obtained via a complete integration of the Pauli equation over time and space. The probability density evolution describes a slipping of the wave packet into two separate packets due to the measurement device, but it cannot account for impacts. We therefore calculate the de Broglie-Bohm trajectories, which not only explain impacts naturally, but also accounts for the spin quantization following the magnetic field gradient. It is then possible to propose a clear explanation of measurement effects in the Stern-Gerlach experiment.
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"abstract": "The Stern-Gerlach experiment is the fundamental experiment in order to\nexhibit the quantization of spin and understand the measurement problem in\nquantum mechanics. However, although the Stern-Gerlach experiment plays an\nessential role in the teaching of quantum mechanics, no complete analysis of\nthis experiment using Pauli spinors is presented in the pedagogical literature.\nThis paper presents such an analysis and develops implications for the theory\nof quantum measurement.\n We first propose an analytic expression of both the wave function and the\nprobability density in the Stern-Gerlach experiment. Our explicit solution is\nobtained via a complete integration of the Pauli equation over time and space.\nThe probability density evolution describes a slipping of the wave packet into\ntwo separate packets due to the measurement device, but it cannot account for\nimpacts.\n We therefore calculate the de Broglie-Bohm trajectories, which not only\nexplain impacts naturally, but also accounts for the spin quantization\nfollowing the magnetic field gradient. It is then possible to propose a clear\nexplanation of measurement effects in the Stern-Gerlach experiment.",
"arxiv_id": "quant-ph/0511276",
"authors": [
"Michel Gondran",
"Alexandre Gondran"
],
"categories": [
"quant-ph"
],
"title": "A complete analysis of the Stern-Gerlach experiment using Pauli spinors",
"url": "https://arxiv.org/abs/quant-ph/0511276"
},
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