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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.


  • Department of Physics, Heze University, Shandong, 274015, PR China


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