Approach to the quantum evolution for underdamped, critically damped, and overdamped driven harmonic oscillators using unitary transformation |
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Authors: | Jeong-Ryeol Choi |
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Affiliation: | Department of New Material Science, Division of Natural Sciences,Sunmoon University, Asan 336-708, South Korea |
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Abstract: | Exact solution of the Schrödinger equation is derived for underdamped, critically damped, and overdamped harmonic oscillators with a driving force. A unitary operator transforming Hamiltonian into a simple form is introduced. The transformed Hamiltonian, represented in terms of a modified frequency ω, is identical with the Hamiltonian of the standard harmonic oscillator for the underdamped oscillator, with the Hamiltonian of a free particle for the critically damped oscillator, and with the Hamiltonian of a system with a harmonic parabolic potential for the overdamped oscillator. The eigenvalues of underdamped oscillator are discrete while those of the critically damped and the overdamped oscillators are continuous. |
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Keywords: | 03.65.Ca 03.65.-w |
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