dorsal/arxiv
View SchemaPhase-Modulus Relations for a Reflected Particle
| Authors | A. Yahalom, R. Englman |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0406190 |
| URL | https://arxiv.org/abs/quant-ph/0406190 |
| Journal | J. Phys. Chem. A, 107(37), 7170 - 7174 (2003) |
Abstract
We formulate analytically the reflection of a one dimensional, expanding free wave-packet (wp) from an infinite barrier. Three types of wp's are considered, representing an electron, a molecule and a classical object. We derive a threshold criterion for the values of the dynamic parameters so that reciprocal (Kramers-Kronig) relations hold {\it in the time domain} between the log-modulus of the wp and the (analytic part of its) phase acquired during the reflection. For an electron, in a typical case, the relations are shown to be satisfied. For a molecule the modulus-phase relations take a more complicated form, including the so called Blaschke term. For a classical particle characterized by a large mean momentum ($\hbar K >> \frac{\hbar trajectory length} {(size of wave-packet)^2} >>> \frac{\hbar}{size of wave-packet}$) the rate of acquisition of the relative phase between different wp components is enormous (for a bullet it is typically $10^{14}$ GHertz) with also a very large value for the phase maximum.
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"abstract": "We formulate analytically the reflection of a one dimensional, expanding free\nwave-packet (wp) from an infinite barrier. Three types of wp\u0027s are considered,\nrepresenting an electron, a molecule and a classical object. We derive a\nthreshold criterion for the values of the dynamic parameters so that reciprocal\n(Kramers-Kronig) relations hold {\\it in the time domain} between the\nlog-modulus of the wp and the (analytic part of its) phase acquired during the\nreflection. For an electron, in a typical case, the relations are shown to be\nsatisfied. For a molecule the modulus-phase relations take a more complicated\nform, including the so called Blaschke term. For a classical particle\ncharacterized by a large mean momentum ($\\hbar K \u003e\u003e \\frac{\\hbar trajectory\nlength} {(size of wave-packet)^2} \u003e\u003e\u003e \\frac{\\hbar}{size of wave-packet}$) the\nrate of acquisition of the relative phase between different wp components is\nenormous (for a bullet it is typically $10^{14}$ GHertz) with also a very large\nvalue for the phase maximum.",
"arxiv_id": "quant-ph/0406190",
"authors": [
"A. Yahalom",
"R. Englman"
],
"categories": [
"quant-ph"
],
"journal_ref": "J. Phys. Chem. A, 107(37), 7170 - 7174 (2003)",
"title": "Phase-Modulus Relations for a Reflected Particle",
"url": "https://arxiv.org/abs/quant-ph/0406190"
},
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