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Curious features of relativistic quantum mechanics in its limit to classical mechanics and application of relativistic coherent states

相对论量子力学对经典力学的限制和相对论相干态的应用的奇怪特征

基本信息

批准号：
08640517
负责人：
TOYAMA Masafumi
金额：
$ 1.09万
依托单位：
Kyoto Sangyo University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
1996
资助国家：
日本
起止时间：
1996 至 1998
项目状态：
已结题

项目摘要

1.We constructed coherent wavepackets of the 'Dirac oscillator' in the usual Dirac representation and in the Foldy-Wouthuysen (FW) representation. In the nonrelativistic limit, these wavepackets are both reduced to Schrolinger's coherent wavepacket for the harmonic oscillator (HO). We found that the wavepacket in the FW representation, although it dissipates in time, behaves much more like a classical particle than in the Dirac representation. Ehrenfest's theorem for the Dirac equation can be obtained, in a natural form, in the FW representation.2.We proposed a method for constructing reflectionless potentials of the Lorentz pseudoscalar (PS) type for the Dirac equation. This is a relativistic generalization of Kay and Moses' inverse scattering method that deals with a similar problem for the Schrodinger equation.3.We showed how the relativistic HO potentials for the Dirac equation can be constructed by means of the inverse scattering method. We revealed that HO potentials are possible for the Lorentz scalar (S) and PS types but not for the vector type.4.We examined the behavior of the nonlinear Dirac soliton in external fields of the S and PS types. We found that for the linear potential of the S type the motion of the soliton centroid is independent of the strength of the nonlinear interaction and this remarkable feature can be understood by means of a version of the so-called collective variable Ansatz (CVA). For external potentials of the PS type, however, we showed that the CVA fails in explaining the behavior of the soliton and the PS potential has no obvious counterpart m classical mechanics. This is related to Zitterbewegung of the soliton centroid in the case of the PS potential.5.We examined the Aharonov-Bohm effect in various time-dependent situations, by means of 'computational quantum dynamics' (CQD). In one of our research plans we will extensively examine mesoscopic electron systems by means of the CQD.

1.在通常的Dirac表象和Foldy-Wouthuysen（FW）表象中构造了“Dirac振子”的相干波包。在非相对论极限下，这些波包都被简化为谐振子的薛林格相干波包。我们发现，在FW表示的波包，虽然它耗散的时间，行为更像一个经典粒子比狄拉克表示。在FW表示中，Dirac方程的Escherichfest定理可以以自然的形式得到。2.提出了一种构造Dirac方程的Lorentz赝标（PS）型无反射势的方法。这是Kay和Moses的逆散射方法的相对论推广，它处理了Schrodinger方程的类似问题。3.我们证明了如何用逆散射方法构造Dirac方程的相对论HO势。我们发现，对于Lorentz标量（S）型和PS型，HO势是可能的，而对于矢量型，HO势是不可能的。4.我们研究了S型和PS型外场中非线性Dirac孤子的行为。我们发现，对于S型线性势，孤子质心的运动与非线性相互作用的强度无关，这一显著的特征可以用一种所谓的集体变量Ancillary（CVA）来理解。然而，对于PS型的外势，我们证明了CVA不能解释孤子的行为，并且PS势在经典力学中没有明显的对应物。这与PS势情况下孤子质心的Zitterbewegung有关。5.我们用计算量子动力学（CQD）方法研究了各种含时情形下的Aharonov-Bohm效应。在我们的一个研究计划中，我们将通过CQD广泛地研究介观电子系统。