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Journal of Physics A Mathematical and General

Larmor precession and dwell time of a relativistic particle scattered by a rectangular quantum well

Zhi-Jian Li, Yi-Hang Nie, J.-Q. Liang, Liang Jiu-Qing

Published May 28, 2003• 4 citations
Publisher

Abstract

The Larmor precession of a relativistic neutral spin-½ particle in a uniform constant magnetic field confined to the region of a one-dimensional rectangular potential well is investigated. The spin precession serves as a clock to measure the time spent by a quantum particle dwelling at a potential well. With the help of a general spin coherent state it is explicitly shown that the spin precession time is equal to the dwell time in the first-order approximation of the infinitesimal field limit. The comparison of the time in a potential well with that in free space shows apparent superluminality.

DOI
10.1088/0305-4470/36/23/319

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The Larmor precession of a relativistic neutral spin-½ particle in a uniform constant magnetic field confined to the region of a one-dimensional rectangular potential well is investigated. The spin precession serves as a clock to measure the time spent by a quantum particle dwelling at a potential well. With the help of a general spin coherent state it is explicitly shown that the spin precession time is equal to the dwell time in the first-order approximation of the infinitesimal field limit. The comparison of the time in a potential well with that in free space shows apparent superluminality.
The Larmor precession of a neutral spinning particle in a magnetic field confined to the region of a one-dimensional rectangular barrier is investigated for both a nonrelativistic and a relativistic incoming particle. The spin precession serves as a clock to measure the time spent by a quantum particle traversing a potential barrier. With the help of a general spin coherent state it is explicitly shown that the precession time is equal to the dwell time in both the nonrelativistic and relativistic cases. We also present a numerical estimation of the precession time showing an apparent superluminal tunneling.
The Larmor precession of a relativistic neutral spin-12\frac{1}{2}21​ particle in a uniform constant magnetic field confined to the region of a one-dimensional arbitrary potential barrier is investigated. The spin precession serves as a clock to measure the time spent by a quantum particle traversing a potential barrier. With the help of a general spin coherent state, it is explicitly shown that the precession time is equal to the dwell time.
We investigate the Larmor precession of a non-relativistic neutral spin-1/2 particle in a uniform constant magnetic field confined to the region of a one-dimensional arbitrary potential barrier.With the help of a general spin coherent state it is explicitly shown that the spin precession time is equal to the dwell time.For the special case of a symmetric rectangular potential barrier,the precession time is also in agreement with the transmission time.We present a numerical estimation of the precession time showing an apparent superluminal tunnelling.
We investigate the Larmor precession of a non-relativistic neutral spin-1/2 particle in a uniform constant magnetic field confined to the region of a one-dimensional arbitrary potential barrier. With the help of a general spin coherent state it is explicitly shown that the spin precession time is equal to the dwell time. For the special case of a symmetric rectangular potential barrier, the precession time is also in agreement with the transmission time. We present a numerical estimation of the precession time showing an apparent superluminal tunnelling.
Baz' and Rybachenko have proposed the use of the Larmor precession as a clock to measure the time it takes a particle to traverse a barrier. An applied magnetic field is confined to the barrier. The spin of the incident particles is polarized perpendicular to this field. The extent of the Larmor precession occurring during transmission is used as a measurement of the time spent traversing the barrier. However, the particles tunneling through an opaque barrier also acquire a spin component parallel to the field since particles with spin parallel to the field have a higher transmission probability than particles with spin antiparallel to the field. Similar effects are actually used to polarize electrons and neutrons. An interpretation of this experiment compares the results with an approach which determines the traversal time by studying transmission of particles through a time-modulated barrier. This leads to three characteristic times describing the interaction of particles with a barrier. A dwell time measures the average time interval during which a particle interacts with the barrier whether it is reflected or transmitted at the end of its stay, a traversal time measures the time interval during which a particle interacts with the barrier if it is finally transmitted, and a reflection time measures the interaction time of a reflected particle.