Coherent, Squeezed, and Thermal State of Harmonic Oscillator with Exponentially Decreasing Frequency
Jeong-Ryeol Choi
Department of New Material Science, Division of Natural Sciences
Sunmoon University, Asan, Republic of Korea
corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.
ABSTRACT
The solutions of Schrödinger equation for a damped harmonic oscillator with exponentially decreasing frequency are derived using invariant operator method. We investigated coherent, squeezed, and thermal states of the system as well as number state. The uncertainty product, quantum-mechanical energy expectation value, and density operator of the system are evaluated. The uncertainty product in coherent state are the same as the minimum uncertainty product in number state. We confirmed that the uncertainty product is always larger than 1/2 in all kinds of states we considered. The mechanical energy expectation value in thermal state decreases in the same way as that in number of state.
INTRODUCTION
The harmonic oscillator played an important role in the development of both theoretical and experimental physics (Dekker 1981). Recently, the investigation of the quantum-mechanical solution for the time-dependent harmonic oscillator (Um et al. 1997), time-dependent forced harmonic oscillator (Um et al. 1996), and asymmetrical quantum sextic anharmonic oscillator (Lee et al. 1998) have been attracted considerable interest as well as their classical analysis. The relations between various results of quantum analysis for the linearly coupled damped harmonic oscillator and their classical property are studied in detail by Dekker (Dekker 1981). . . .
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