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Quantum Analysis on Time Behavior of a Lengthening Pendulum


Affiliations
1 Department of Radiologic Technology, Daegu Health College, Buk-gu, Daegu 41453, Korea, Democratic People's Republic of
 

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 eigen values, 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 θ at t = 0 oscillates back and forth from the center (θ = 0). 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.
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  • Quantum Analysis on Time Behavior of a Lengthening Pendulum

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Authors

Jeong Ryeol Choi
Department of Radiologic Technology, Daegu Health College, Buk-gu, Daegu 41453, Korea, Democratic People's Republic of
Ji Nny Song
Department of Radiologic Technology, Daegu Health College, Buk-gu, Daegu 41453, Korea, Democratic People's Republic of

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 eigen values, 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 θ at t = 0 oscillates back and forth from the center (θ = 0). 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.