1993 Fiscal Year Final Research Report Summary
Quantum Dynamics and Non-Inertial Frames of Reference.
| Project/Area Number |
03640327
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| Research Category |
Grant-in-Aid for General Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Research Field |
物性一般（含極低温･固体物性に対する理論）
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| Research Institution | TOHOKU UNIVERSITY |
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Principal Investigator |
TAKAGI Shin Tohoku Univ. Faculty of Science, Assiatant Professor, 理学部, 助教授 (90124594)
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| Project Period (FY) |
1991 – 1993
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| Keywords | Quantum mechanics / Non-inertial frames / Dilating frame / Harmonic oscillator / Squeezed states / Aharonov-Bohm effects / Berry's phase / Tunnelling time |
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| Research Abstract |
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.
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