dorsal/arxiv
View SchemaAsymptotes and characteristic times for transmission and reflection
| Authors | N. L. Chuprikov |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0301113 |
| URL | https://arxiv.org/abs/quant-ph/0301113 |
Abstract
A complete one-dimensional scattering of a spinless particle on a time-independent potential barrier is considered. To describe separately transmitted and reflected particles in the corresponding subsets of identical experiments, we introduce the notions of scattering channels for transmission and reflection. We find for both channels the (unitary) scattering matrices and reconstruct, by known out asymptotes (i.e., by the transmitted and reflected wave packets), the corresponding in asymptotes. Unlike the out asymptotes for transmission and reflection, their in asymptotes represent nonorthogonal functions. As is shown, the position distributions of to-be-transmitted and to-be-reflected particles, except their average positions, are unpredictable. At the same time, the momentum distributions of these particles are physically meaningful and can be observed to the full. We show that both the subensembles of particles must start (on the average) from the same spatial point, and the momentum distributions of to-be-scattered and scattered particles must be the same for each scattering channel. Taking into account these properties, we define the (individual) delay times for transmission and reflection for wave packets of an arbitrary width. Besides, to estimate the duration of the scattering event, we derive the expression for a (total) scattering time.
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"abstract": "A complete one-dimensional scattering of a spinless particle on a\ntime-independent potential barrier is considered. To describe separately\ntransmitted and reflected particles in the corresponding subsets of identical\nexperiments, we introduce the notions of scattering channels for transmission\nand reflection. We find for both channels the (unitary) scattering matrices and\nreconstruct, by known out asymptotes (i.e., by the transmitted and reflected\nwave packets), the corresponding in asymptotes. Unlike the out asymptotes for\ntransmission and reflection, their in asymptotes represent nonorthogonal\nfunctions. As is shown, the position distributions of to-be-transmitted and\nto-be-reflected particles, except their average positions, are unpredictable.\nAt the same time, the momentum distributions of these particles are physically\nmeaningful and can be observed to the full. We show that both the subensembles\nof particles must start (on the average) from the same spatial point, and the\nmomentum distributions of to-be-scattered and scattered particles must be the\nsame for each scattering channel. Taking into account these properties, we\ndefine the (individual) delay times for transmission and reflection for wave\npackets of an arbitrary width. Besides, to estimate the duration of the\nscattering event, we derive the expression for a (total) scattering time.",
"arxiv_id": "quant-ph/0301113",
"authors": [
"N. L. Chuprikov"
],
"categories": [
"quant-ph"
],
"title": "Asymptotes and characteristic times for transmission and reflection",
"url": "https://arxiv.org/abs/quant-ph/0301113"
},
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