dorsal/arxiv
View SchemaComplementarity of representations in quantum mechanics
| Authors | Hans Halvorson |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0110102 |
| URL | https://arxiv.org/abs/quant-ph/0110102 |
| DOI | 10.1016/j.shpsb.2003.01.001 |
| Journal | Studies in History and Philosophy of Modern Physics 35, 45-56 (2004) |
Abstract
We show that Bohr's principle of complementarity between position and momentum descriptions can be formulated rigorously as a claim about the existence of representations of the CCRs. In particular, in any representation where the position operator has eigenstates, there is no momentum operator, and vice versa. Equivalently, if there are nonzero projections corresponding to sharp position values, all spectral projections of the momentum operator map onto the zero element.
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"abstract": "We show that Bohr\u0027s principle of complementarity between position and\nmomentum descriptions can be formulated rigorously as a claim about the\nexistence of representations of the CCRs. In particular, in any representation\nwhere the position operator has eigenstates, there is no momentum operator, and\nvice versa. Equivalently, if there are nonzero projections corresponding to\nsharp position values, all spectral projections of the momentum operator map\nonto the zero element.",
"arxiv_id": "quant-ph/0110102",
"authors": [
"Hans Halvorson"
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"doi": "10.1016/j.shpsb.2003.01.001",
"journal_ref": "Studies in History and Philosophy of Modern Physics 35, 45-56\n (2004)",
"title": "Complementarity of representations in quantum mechanics",
"url": "https://arxiv.org/abs/quant-ph/0110102"
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