A concise quantum mechanical treatment of the forced damped harmonic oscillator

Ti Li 1
  • 1 Department of Physics, Heze University, Shandong, 274015, PR China

Abstract

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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  • [1] H. Dekker, Z. Phys. B 21, 295 (1975) http://dx.doi.org/10.1007/BF01313310

  • [2] J.R. Choi, Rep. Math. Phys. 52, 321 (2003) http://dx.doi.org/10.1016/S0034-4877(03)80032-0

  • [3] R.W. Hasse, J. Math. Phys. 16, 2011 (1975) http://dx.doi.org/10.1063/1.522431

  • [4] H.G. Oh, H.R. Lee, T.F. George, C.I. Um, Phys. Rev. A 39, 5515 (1989) http://dx.doi.org/10.1103/PhysRevA.39.5515

  • [5] H. Gzyl, Phys. Rev. A 27, 2297 (1983) http://dx.doi.org/10.1103/PhysRevA.27.2297

  • [6] K.H. Yeon et al., J. Phys. A-Math. Gen. 34, 7719 (2001) http://dx.doi.org/10.1088/0305-4470/34/37/321

  • [7] C.I. Um, K.H. Yeon, T.F. George, Phys. Rep. 362, 63 (2002) http://dx.doi.org/10.1016/S0370-1573(01)00077-1

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