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Jeong Ryeol Choi ¹, Ji Nny Song ¹

Affiliations
1 Department of Radiologic Technology, Daegu Health College, Buk-gu, Daegu 41453, KP

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.

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Jeong Ryeol Choi ¹, Ji Nny Song ¹, Yeontaek Choi ²

Affiliations
1 Department of Radiologic Technology, Daegu Health College, Yeongsong-ro 15, Buk-gu, Daegu 702-722, KR
2 Division of Mathematical Modeling, National Institute for Mathematical Sciences, KTDaeduk 2 Research Center, 463-1 Jeonmin-dong, Yuseong-gu, Daejeon 305-390, KR

Abstract

Density operator of oscillatory optical systems with time-dependent parameters is analyzed. In this case, a system is described by a time-dependent Hamiltonian. Invariant operator theory is introduced in order to describe time-varying behavior of the system. Due to the time dependence of parameters, the frequency of oscillation, so-called a modified frequency of the system, is somewhat different from the natural frequency. In general, density operator of a time-dependent optical system is represented in terms of the modified frequency.We showed how to determine density operator of complicated time-dependent optical systems in thermal state. Usually, density operator description of quantum states is more general than the one described in terms of the state vector.

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