dorsal/arxiv
View SchemaTemporal aspects of one-dimensional completed scattering: An alternative view
| Authors | N L Chuprikov |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0511024 |
| URL | https://arxiv.org/abs/quant-ph/0511024 |
Abstract
A {\it completed} scattering of a particle on a static one-dimensional (1D) potential barrier is a combined quantum process to consist from two elementary sub-processes (transmission and reflection) evolved coherently at all stages of scattering and macroscopically distinct at the final stage. The existing model of the process is clearly inadequate to its nature: all one-particle "observables" and "tunneling times", introduced as quantities to be common for the sub-processes, cannot be experimentally measured and, consequently, have no physical meaning; on the contrary, quantities introduced for either sub-process have no basis, for the time evolution of either sub-process is unknown in this model. We show that the wave function to describe a completed scattering can be uniquely presented as the sum of two solutions to the Schr\"odinger equation, which describe separately the sub-processes at all stages of scattering. For symmetric potential barriers such solutions are found explicitly. For either sub-process we define the time spent, on the average, by a particle in the barrier region. We define it as the Larmor time. As it turned out, this time is just Buttiker's dwell time averaged over the corresponding localized state. Thus, firstly, we justify the known definition of the local dwell time introduced by Hauge and co-workers as well by Leavens and Aers, for now this time can be measured; secondly, we confirm that namely Buttiker's dwell time gives the energy-distribution for the tunneling time; thirdly, we state that all the definitions are valid only if they are based on the wave functions for transmission and reflection found in our paper. Besides, we define the exact and asymptotic group times to be auxiliary in timing the scattering process.
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"abstract": "A {\\it completed} scattering of a particle on a static one-dimensional (1D)\npotential barrier is a combined quantum process to consist from two elementary\nsub-processes (transmission and reflection) evolved coherently at all stages of\nscattering and macroscopically distinct at the final stage. The existing model\nof the process is clearly inadequate to its nature: all one-particle\n\"observables\" and \"tunneling times\", introduced as quantities to be common for\nthe sub-processes, cannot be experimentally measured and, consequently, have no\nphysical meaning; on the contrary, quantities introduced for either sub-process\nhave no basis, for the time evolution of either sub-process is unknown in this\nmodel. We show that the wave function to describe a completed scattering can be\nuniquely presented as the sum of two solutions to the Schr\\\"odinger equation,\nwhich describe separately the sub-processes at all stages of scattering. For\nsymmetric potential barriers such solutions are found explicitly. For either\nsub-process we define the time spent, on the average, by a particle in the\nbarrier region. We define it as the Larmor time. As it turned out, this time is\njust Buttiker\u0027s dwell time averaged over the corresponding localized state.\nThus, firstly, we justify the known definition of the local dwell time\nintroduced by Hauge and co-workers as well by Leavens and Aers, for now this\ntime can be measured; secondly, we confirm that namely Buttiker\u0027s dwell time\ngives the energy-distribution for the tunneling time; thirdly, we state that\nall the definitions are valid only if they are based on the wave functions for\ntransmission and reflection found in our paper. Besides, we define the exact\nand asymptotic group times to be auxiliary in timing the scattering process.",
"arxiv_id": "quant-ph/0511024",
"authors": [
"N L Chuprikov"
],
"categories": [
"quant-ph",
"cond-mat.mes-hall"
],
"title": "Temporal aspects of one-dimensional completed scattering: An alternative view",
"url": "https://arxiv.org/abs/quant-ph/0511024"
},
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"variant": "snapshot-2026-03-01",
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