dorsal/arxiv
View SchemaQuantised Three-Pillar Problem
| Authors | Carl M. Bender, Dorje C. Brody, Bernhard K. Meister |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0302097 |
| URL | https://arxiv.org/abs/quant-ph/0302097 |
Abstract
This paper examines the quantum mechanical system that arises when one quantises a classical mechanical configuration described by an underdetermined system of equations. Specifically, we consider the well-known problem in classical mechanics in which a beam is supported by three identical rigid pillars. For this problem it is not possible to calculate uniquely the forces supplied by each pillar. However, if the pillars are replaced by springs, then the forces are uniquely determined. The three-pillar problem and its associated indeterminacy is recovered in the limit as the spring constant tends to infinity. In this paper the spring version of the problem is quantised as a constrained dynamical system. It is then shown that as the spring constant becomes large, the quantum analog of the ambiguity reemerges as a kind of quantum anomaly.
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"abstract": "This paper examines the quantum mechanical system that arises when one\nquantises a classical mechanical configuration described by an underdetermined\nsystem of equations. Specifically, we consider the well-known problem in\nclassical mechanics in which a beam is supported by three identical rigid\npillars. For this problem it is not possible to calculate uniquely the forces\nsupplied by each pillar. However, if the pillars are replaced by springs, then\nthe forces are uniquely determined. The three-pillar problem and its associated\nindeterminacy is recovered in the limit as the spring constant tends to\ninfinity. In this paper the spring version of the problem is quantised as a\nconstrained dynamical system. It is then shown that as the spring constant\nbecomes large, the quantum analog of the ambiguity reemerges as a kind of\nquantum anomaly.",
"arxiv_id": "quant-ph/0302097",
"authors": [
"Carl M. Bender",
"Dorje C. Brody",
"Bernhard K. Meister"
],
"categories": [
"quant-ph"
],
"title": "Quantised Three-Pillar Problem",
"url": "https://arxiv.org/abs/quant-ph/0302097"
},
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