Table of Contents
Physics Research International
Volume 2016, Article ID 1696105, 9 pages
http://dx.doi.org/10.1155/2016/1696105
Review Article

Quantum Analysis on Time Behavior of a Lengthening Pendulum

Department of Radiologic Technology, Daegu Health College, Buk-gu, Daegu 41453, Republic of Korea

Received 22 August 2015; Accepted 26 October 2015

Academic Editor: Ashok Chatterjee

Copyright © 2016 Jeong Ryeol Choi and Ji Nny Song. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Quantum properties of a lengthening pendulum are studied under the assumption that the length of the string increases at a steady rate. Advanced analysis for various physical problems in several types of quantum states, such as propagators, Wigner distribution functions, energy eigenvalues, probability densities, and dispersions of physical quantities, is carried out using quantum wave functions of the system. In particular, the time behavior of Gaussian-type wave packets is investigated in detail. The probability density for a Gaussian wave packet displaced in the positive at oscillates back and forth from the center (). This phenomenon is very similar to the classical motion of the pendulum. As a consequence, we can confirm that there is a correspondence between its quantum and classical behaviors. When we analyze a dynamical system in view of quantum mechanics, the quantum and classical correspondence is very important in order for the associated quantum theory to be valid and viable.