A concise quantum mechanical treatment of the forced damped harmonic oscillator

• Authors: Ti Li
• Languages of publication: EN

Abstracts

EN

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.

Keywords

EN

wave function; forced damped oscillator; generalized coordinate; eigenfunction of generalized coordinate operator; representation

Discipline

• 03.65.-w: Quantum mechanics[see also 03.67.-a Quantum information; 05.30.-d Quantum statistical mechanics; 31.30.J- Relativistic and quantum electrodynamics (QED) effects in atoms, molecules, and ions in atomic physics]
• 03.65.Ge: Solutions of wave equations: bound states

• Publisher: De Gruyter Open
• Journal: Open Physics
• Year: 2008
• Volume: 6
• Issue: 4
• Pages: 891-894

Dates

published

1 - 12 - 2008

online

27 - 9 - 2008

Contributors

author

Ti Li

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

References

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Identifiers

DOI

10.2478/s11534-008-0105-2