dorsal/arxiv
View SchemaIs PT-symmetric quantum mechanics just quantum mechanics in a non-orthogonal basis?
| Authors | Damien Martin |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0701223 |
| URL | https://arxiv.org/abs/quant-ph/0701223 |
Abstract
One of the postulates of quantum mechanics is that the Hamiltonian is Hermitian, as this guarantees that the eigenvalues are real. Recently there has been an interest in asking if $H^\dagger = H$ is a necessary condition, and has lead to the development of PT-symmetric quantum mechanics. This note shows that any finite physically acceptable non-Hermitian Hamiltonian is equivalent to doing ordinary quantum mechanics in a non-orthogonal basis. In particular, this means that there is no experimental distinction between PT-symmetric quantum mechanics and ordinary quantum mechanics for finite systems. In particular, the claim that PT-symmetric quantum mechanics allows for faster evolution than Hermitian quantum mechanics is shown to be a problem of physical interpretation.
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"abstract": "One of the postulates of quantum mechanics is that the Hamiltonian is\nHermitian, as this guarantees that the eigenvalues are real. Recently there has\nbeen an interest in asking if $H^\\dagger = H$ is a necessary condition, and has\nlead to the development of PT-symmetric quantum mechanics. This note shows that\nany finite physically acceptable non-Hermitian Hamiltonian is equivalent to\ndoing ordinary quantum mechanics in a non-orthogonal basis. In particular, this\nmeans that there is no experimental distinction between PT-symmetric quantum\nmechanics and ordinary quantum mechanics for finite systems. In particular, the\nclaim that PT-symmetric quantum mechanics allows for faster evolution than\nHermitian quantum mechanics is shown to be a problem of physical\ninterpretation.",
"arxiv_id": "quant-ph/0701223",
"authors": [
"Damien Martin"
],
"categories": [
"quant-ph",
"hep-th"
],
"title": "Is PT-symmetric quantum mechanics just quantum mechanics in a non-orthogonal basis?",
"url": "https://arxiv.org/abs/quant-ph/0701223"
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