dorsal/arxiv
View SchemaFrom the paradoxes of the standard wave-packet analysis to the definition of tunneling times for particles
| Authors | N. L. Chuprikov |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0106129 |
| URL | https://arxiv.org/abs/quant-ph/0106129 |
Abstract
We develop a new variant of the wave-packet analysis and solve the tunneling time problem for one particle. Our approach suggests an individual asymptotic description of the quantum subensembles of transmitted and reflected particles both at the final and initial stage of tunneling. We find the initial states of both subensembles, which are non-orthogonal. The latter reflects ultimately the fact that at the initial stage of tunneling it is impossible to predict whether a particle will be transmitted through or reflected off the barrier. At the same time, in this case, one can say about the to-be-transmitted and to-be-reflected subensembles of particles. We show that before the interaction of the incident packet with the barrier both the number of particles and the expectation value of the particle's momentum are constant for each subensemble. Besides, these asymptotic quantities coincide with those of the corresponding scattered subensemble. On the basis of this formalism we define individual delay times for both scattering channels. Taking into account the spreading of wave packets, we define the low bound of the scattering time to describe the whole quantum ensemble of particles. All three characteristic times are derived in terms of the expectation values of the position and momentum operators. The condition which must be fulfilled for completed scattering events is derived. We propose also the scheme of a {\it gedanken} experiment that allows one to verify our approach.
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"abstract": "We develop a new variant of the wave-packet analysis and solve the tunneling\ntime problem for one particle. Our approach suggests an individual asymptotic\ndescription of the quantum subensembles of transmitted and reflected particles\nboth at the final and initial stage of tunneling. We find the initial states of\nboth subensembles, which are non-orthogonal. The latter reflects ultimately the\nfact that at the initial stage of tunneling it is impossible to predict whether\na particle will be transmitted through or reflected off the barrier. At the\nsame time, in this case, one can say about the to-be-transmitted and\nto-be-reflected subensembles of particles. We show that before the interaction\nof the incident packet with the barrier both the number of particles and the\nexpectation value of the particle\u0027s momentum are constant for each subensemble.\nBesides, these asymptotic quantities coincide with those of the corresponding\nscattered subensemble. On the basis of this formalism we define individual\ndelay times for both scattering channels. Taking into account the spreading of\nwave packets, we define the low bound of the scattering time to describe the\nwhole quantum ensemble of particles. All three characteristic times are derived\nin terms of the expectation values of the position and momentum operators. The\ncondition which must be fulfilled for completed scattering events is derived.\nWe propose also the scheme of a {\\it gedanken} experiment that allows one to\nverify our approach.",
"arxiv_id": "quant-ph/0106129",
"authors": [
"N. L. Chuprikov"
],
"categories": [
"quant-ph"
],
"title": "From the paradoxes of the standard wave-packet analysis to the definition of tunneling times for particles",
"url": "https://arxiv.org/abs/quant-ph/0106129"
},
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