dorsal/arxiv
View SchemaClassical Representations of Quantum Mechanics Related to Statistically Complete Observables
| Authors | Werner Stulpe |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0610122 |
| URL | https://arxiv.org/abs/quant-ph/0610122 |
Abstract
We present a reformulation of quantum mechanics in terms of probability measures and functions on a general classical sample space and in particular in terms of probability densities and functions on phase space. The basis of our proceeding is the existence of so-called statistically complete observables and the duality between the state spaces and the spaces of the observables, the latter holding in the quantum as well as in the classical case. In the phase-space context, we further discuss joint position-momentum observables, Hilbert spaces of infinitely differentiable functions on phase space, and dequantizations. Finally, the relation of quantum dynamics to the classical Liouville dynamics is investigated.
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"abstract": "We present a reformulation of quantum mechanics in terms of probability\nmeasures and functions on a general classical sample space and in particular in\nterms of probability densities and functions on phase space. The basis of our\nproceeding is the existence of so-called statistically complete observables and\nthe duality between the state spaces and the spaces of the observables, the\nlatter holding in the quantum as well as in the classical case. In the\nphase-space context, we further discuss joint position-momentum observables,\nHilbert spaces of infinitely differentiable functions on phase space, and\ndequantizations. Finally, the relation of quantum dynamics to the classical\nLiouville dynamics is investigated.",
"arxiv_id": "quant-ph/0610122",
"authors": [
"Werner Stulpe"
],
"categories": [
"quant-ph"
],
"title": "Classical Representations of Quantum Mechanics Related to Statistically Complete Observables",
"url": "https://arxiv.org/abs/quant-ph/0610122"
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