Quantum-classical correspondence for the inverted oscillator

发布时间：2018-01-14 02:18

本文关键词：Quantum-classical correspondence for the inverted oscillator　出处：《Chinese Physics C》2017年11期 　论文类型：期刊论文

【摘要】：While quantum-classical correspondence for a system is a very fundamental problem in modern physics,the understanding of its mechanism is often elusive,so the methods used and the results of detailed theoretical analysis have been accompanied by active debate.In this study,the differences and similarities between quantum and classical behavior for an inverted oscillator have been analyzed based on the description of a complete generalized Airy function-type quantum wave solution.The inverted oscillator model plays an important role in several branches of cosmology and particle physics.The quantum wave packet of the system is composed of many sub-packets that are localized at different positions with regular intervals between them.It is shown from illustrations of the probability density that,although the quantum trajectory of the wave propagation is somewhat different from the corresponding classical one,the difference becomes relatively small when the classical excitation is sufficiently high.We have confirmed that a quantum wave packet moving along a positive or negative direction accelerates over time like a classical wave.From these main interpretations and others in the text,we conclude that our theory exquisitely illustrates quantum and classical correspondence for the system,which is a crucial concept in quantum mechanics.
[Abstract]:While quantum-classical correspondence for a system is a very fundamental problem in modern physics,the understanding of its mechanism is often elusive,so the methods used and the results of detailed theoretical analysis have been accompanied by active debate.In this study,the differences and similarities between quantum and classical behavior for an inverted oscillator have been analyzed based on the description of a complete generalized Airy function-type quantum wave solution.The inverted oscillator model plays an important role in several branches of cosmology and particle physics.The quantum wave packet of the system is composed of many sub-packets that are localized at different positions with regular intervals between them.It is shown from illustrations of the probability density that,although the quantum trajectory of the wave propagation is somewhat different from the corresponding classical one,the difference becomes relatively small when the classical excitation is sufficiently high.We have confirmed that a quantum wave packet moving along a positive or negative direction accelerates over time like a classical wave.From these main interpretations and others in the text,we conclude that our theory exquisitely illustrates quantum and classical correspondence for the system,which is a crucial concept in quantum mechanics.
【作者单位】： Laboratoire
【基金】：Supported by the Basic Science Research Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Education(NRF-2016R1D1A1A09919503)
【分类号】：O413;TN752
【正文快照】： 1 IntroductionThere has been a surge of interest in studying quan-tum properties and their correspondence[1]with clas-sical properties for various mechanical systems beyondbound systems[2 4].The correspondence of quantumand classical mechanics is crucia

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