dorsal/arxiv
View SchemaComment on Complex Extension of Quantum Mechanics
| Authors | Ali Mostafazadeh |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0407070 |
| URL | https://arxiv.org/abs/quant-ph/0407070 |
Abstract
In their Erratum [Phys. Rev. Lett. {\bf 92}, 119902 (2004), quant-ph/0208076], written in reaction to [quant-ph/0310164], Bender, Brody and Jones propose a revised definition for a physical observable in PT-symmetric quantum mechanics. We show that although this definition avoids the dynamical inconsistency revealed in quant-ph/0310164, it is still not a physically viable definition. In particular, we point out that a general proof that this definition is consistent with the requirements of the quantum measurement theory is lacking, give such a proof for a class of PT-symmetric systems by establishing the fact that this definition implies that the observables are pseudo-Hermitian operators, and show that for all the cases that this definition is consistent with the requirements of measurement theory it reduces to a special case of a more general definition given in [quant-ph/0310164]. The latter is the unique physically viable definition of observables in PT-symmetric quantum mechanics.
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"abstract": "In their Erratum [Phys. Rev. Lett. {\\bf 92}, 119902 (2004),\nquant-ph/0208076], written in reaction to [quant-ph/0310164], Bender, Brody and\nJones propose a revised definition for a physical observable in PT-symmetric\nquantum mechanics. We show that although this definition avoids the dynamical\ninconsistency revealed in quant-ph/0310164, it is still not a physically viable\ndefinition. In particular, we point out that a general proof that this\ndefinition is consistent with the requirements of the quantum measurement\ntheory is lacking, give such a proof for a class of PT-symmetric systems by\nestablishing the fact that this definition implies that the observables are\npseudo-Hermitian operators, and show that for all the cases that this\ndefinition is consistent with the requirements of measurement theory it reduces\nto a special case of a more general definition given in [quant-ph/0310164]. The\nlatter is the unique physically viable definition of observables in\nPT-symmetric quantum mechanics.",
"arxiv_id": "quant-ph/0407070",
"authors": [
"Ali Mostafazadeh"
],
"categories": [
"quant-ph",
"hep-th",
"math-ph",
"math.MP"
],
"title": "Comment on Complex Extension of Quantum Mechanics",
"url": "https://arxiv.org/abs/quant-ph/0407070"
},
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