• Jeong-Ryeol Choi

      Articles written in Pramana – Journal of Physics

    • Thermal state of the general time-dependent harmonic oscillator

      Jeong-Ryeol Choi

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      Taking advantage of dynamical invariant operator, we derived quantum mechanical solution of general time-dependent harmonic oscillator. The uncertainty relation of the system is always larger than ħ/2 not only in number but also in the thermal state as expected. We used the diagonal elements of density operator satisfying Leouville-von Neumann equation to calculate various expectation values in the thermal state. We applied our theory to a special case which is the forced Caldirola-Kanai oscillator.

    • Quantum states with continuous spectrum for a general time-dependent oscillator

      Jeong-Ryeol Choi

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      We investigated quantum states with continuous spectrum for a general time-dependent oscillator using invariant operator and unitary transformation methods together. The form of the transformed invariant operator by a unitary operator is the same as the Hamiltonian of the simple harmonic oscillator:I’ = p2/2 +ω2q2/2. The fact thatω2 of the transformed invariant operator is constant enabled us to investigate the system separately for three cases, whereω2 > 0,ω2 < 0, andω2 = 0. The eigenstates of the system are discrete forω2 > 0. On the other hand, forω2 <− 0, the eigenstates are continuous. The time-dependent oscillators whose spectra of the wave function are continuous are not oscillatory. The wave function forω2 < 0 is expressed in terms of the parabolic cylinder function. We applied our theory to the driven harmonic oscillator with strongly pulsating mass.

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