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Quantum Dynamics and Non-Inertial Frames of Reference.

量子动力学和非惯性参考系。

基本信息

批准号：
03640327
负责人：
TAKAGI Shin
金额：
$ 0.9万
依托单位：
TOHOKU UNIVERSITY
依托单位国家：
日本
项目类别：
Grant-in-Aid for General Scientific Research (C)
财政年份：
1991
资助国家：
日本
起止时间：
1991 至 1993
项目状态：
已结题

项目摘要

The use of non-inertial frames in solving time-dependent Schroedinger equation (TDSE) for a one-particle system has lead to new insights and intuitive undestanding of some known facts as well as to development of new types of problems and results. Non-inertial frames are generally associated with inertial forces which are absent in the inertial frame. In particular in the dilating frame(Df), where space expands or contracts uniformly, the associated inertial force turns out to be harmonic. This may be understood by recalling Hubble's law in cosmology, and has lead to the equivalence theorem(ET) that the TDSE for harmonic oscillator(HO) can be transformed to the TDSE for the free particle in an appropriately chosen DF.The ET has enabled us to pictorially understand such important HO quantum states as time-dependent coherent states or squeezed states ; viewed from a DF they are nothing but free Gaussian packets. It has also enabled us to construct analytically in a closed form such interesting wave packets as pulsating spherical packets, which are extremely hard to obtain in a conventional method. Furthermore, with the aid of linearly accelerated frames and rotating frames, the TDSE for a charged particle in spatially uniform time-dependent electromagnetic field has been transformed to the TDSE for a HO.Similar results have been shown to apply to the Non-linear Schroedinger Field Equation and to the soliton motion thereof. Related considerations and techniques have been applied to Aharonov-Bohm(AB) effect, thereby revealing subtle difference between the AB phase and the corresponding Berry's phase, to an electrically-neutral particle confined to a twisted quantum-wire loop, which has been shown to experience a "geometry-induced AB-like effect", where the torsion of the wire plays the role of the vector postential, to a scrutiny of the notion of the so-called tunnelling time, and so forth.

在单质点系统的含时薛定谔方程(TDSE)的求解中，非惯性标架的使用带来了对一些已知事实的新见解和直观理解，以及新类型问题和结果的发展。非惯性系通常与惯性系中没有的惯性力有关。特别是在空间均匀伸展或收缩的膨胀框架(DF)中，与之相关的惯性力被证明是简谐的。这可以通过回顾宇宙学中的哈勃定律来理解，并导致了等价定理(ET)，即在适当选择的DF中，谐振子(HO)的TDSE可以转换为自由粒子的TDSE。该定理使我们能够图形化地理解含时相干态或压缩态等重要的HO量子态；从DF看，它们只不过是自由高斯包。它还使我们能够以封闭的形式解析地构造一些有趣的波包，如脉动球形波包，这在传统方法中是很难获得的。此外，借助于线性加速标架和旋转标架，将空间均匀时变电磁场中带电粒子的TDSE变换为HO的TDSE。类似的结果也适用于非线性薛定谔场方程及其孤子运动。相关的考虑和技术已经被应用于Aharonov-Bohm(AB)效应，从而揭示了AB相和相应的Berry相之间的细微差别，揭示了限制在扭曲的量子线环中的电中性粒子，已经被证明经历了“几何诱导的AB效应”，其中线的扭转扮演了矢量后势的角色，对所谓的隧道时间的概念的审查，等等。