Abstract
A many-body system consisting of a central elastically bound particle coupled to a large number of harmonic oscillators is studied. The co-ordinate of this particle satisfies the equation of motion of a damped harmonic oscillator. To get the quantal description of this damped motion, the many-body wave function for the complete system is written in the coherent-state basis,i.e. as a product of a real stationary wave function and a co-ordinate- and time-dependent phase factor. In order to isolate the motion of the central particle, the stationary wave function is approximated by a product of single-particle wave functions. By calculating the contribution of the variable phase factor to the single-particle wave function, it is shown that the resulting equation for the damped motion of an oscillator is the Schrodinger-Langevin equation.
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