dorsal/arxiv
View SchemaWave functions and tunneling times for one-dimensional transmission and reflection
| Authors | N. L. Chuprikov |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0311090 |
| URL | https://arxiv.org/abs/quant-ph/0311090 |
Abstract
It is shown that in the case of the one-particle one-dimensional scattering problem for a given time-independent potential, for each state of the whole quantum ensemble of identically prepared particles, there is an unique pair of (subensemble's) solutions to the Schr\"odinger equation, which, as we postulate, describe separately transmission and reflection: in the case of nonstationary states, for any instant of time, these functions are orthogonal and their sum describes the state of all particles; evolving with constant norms, one of them approaches at late times the transmitted wave packet and another approaches the reflected packet. Both for transmission and reflection, 1) well before and after the scattering event, the average kinetic energy of particles is the same, 2) the average starting point differs, in the general case, from that for all particles. It is shown that for reflection, in the case of symmetric potential barriers, the domain of the motion of particles is bounded by the midpoint of the barrier region. We define (exact and asymptotic) transmission and reflection times and show that the basic results of our formalism can be, in principle, checked experimentally.
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"abstract": "It is shown that in the case of the one-particle one-dimensional scattering\nproblem for a given time-independent potential, for each state of the whole\nquantum ensemble of identically prepared particles, there is an unique pair of\n(subensemble\u0027s) solutions to the Schr\\\"odinger equation, which, as we\npostulate, describe separately transmission and reflection: in the case of\nnonstationary states, for any instant of time, these functions are orthogonal\nand their sum describes the state of all particles; evolving with constant\nnorms, one of them approaches at late times the transmitted wave packet and\nanother approaches the reflected packet. Both for transmission and reflection,\n1) well before and after the scattering event, the average kinetic energy of\nparticles is the same, 2) the average starting point differs, in the general\ncase, from that for all particles. It is shown that for reflection, in the case\nof symmetric potential barriers, the domain of the motion of particles is\nbounded by the midpoint of the barrier region. We define (exact and asymptotic)\ntransmission and reflection times and show that the basic results of our\nformalism can be, in principle, checked experimentally.",
"arxiv_id": "quant-ph/0311090",
"authors": [
"N. L. Chuprikov"
],
"categories": [
"quant-ph"
],
"title": "Wave functions and tunneling times for one-dimensional transmission and reflection",
"url": "https://arxiv.org/abs/quant-ph/0311090"
},
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