dorsal/arxiv
View SchemaProbability distribution of arrival times in quantum mechanics
| Authors | V. Delgado |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9709037 |
| URL | https://arxiv.org/abs/quant-ph/9709037 |
| DOI | 10.1103/PhysRevA.57.762 |
| Journal | Phys.Rev.A57:762,1998 |
Abstract
In a previous paper [V. Delgado and J. G. Muga, Phys. Rev. A 56, 3425 (1997)] we introduced a self-adjoint operator $\hat {{\cal T}}(X)$ whose eigenstates can be used to define consistently a probability distribution of the time of arrival at a given spatial point. In the present work we show that the probability distribution previously proposed can be well understood on classical grounds in the sense that it is given by the expectation value of a certain positive definite operator $\hat J^{(+)}(X)$ which is nothing but a straightforward quantum version of the modulus of the classical current. For quantum states highly localized in momentum space about a certain momentum $p_0 \neq 0$, the expectation value of $\hat J^{(+)}(X)$ becomes indistinguishable from the quantum probability current. This fact may provide a justification for the common practice of using the latter quantity as a probability distribution of arrival times.
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"abstract": "In a previous paper [V. Delgado and J. G. Muga, Phys. Rev. A 56, 3425 (1997)]\nwe introduced a self-adjoint operator $\\hat {{\\cal T}}(X)$ whose eigenstates\ncan be used to define consistently a probability distribution of the time of\narrival at a given spatial point. In the present work we show that the\nprobability distribution previously proposed can be well understood on\nclassical grounds in the sense that it is given by the expectation value of a\ncertain positive definite operator $\\hat J^{(+)}(X)$ which is nothing but a\nstraightforward quantum version of the modulus of the classical current. For\nquantum states highly localized in momentum space about a certain momentum $p_0\n\\neq 0$, the expectation value of $\\hat J^{(+)}(X)$ becomes indistinguishable\nfrom the quantum probability current. This fact may provide a justification for\nthe common practice of using the latter quantity as a probability distribution\nof arrival times.",
"arxiv_id": "quant-ph/9709037",
"authors": [
"V. Delgado"
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"quant-ph"
],
"doi": "10.1103/PhysRevA.57.762",
"journal_ref": "Phys.Rev.A57:762,1998",
"title": "Probability distribution of arrival times in quantum mechanics",
"url": "https://arxiv.org/abs/quant-ph/9709037"
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