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Open Physics

2008 | 6 | 4 | 891-894
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A concise quantum mechanical treatment of the forced damped harmonic oscillator

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By selecting a right generalized coordinate X, which contains the general solutions of the classical motion equation of a forced damped harmonic oscillator, we obtain a simple Hamiltonian which does not contain time for the oscillator such that Schrödinger equation and its solutions can be directly written out in X representation. The wave functin in x representation are also given with the help of the eigenfunctions of the operator $$\hat X$$ in x representation. The evolution of $$\left\langle {\hat x} \right\rangle$$ is the same as in the classical mechanics, and the uncertainty in position is independent of an external influence; one part of energy mean is quantized and attenuated, and the other is equal to the classical energy.
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891-894
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1 - 12 - 2008
online
27 - 9 - 2008
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References
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