Abstract
A partial integro-differential equation is formulated for the Wigner transform of the quantum mechanical reduced density operator describing the time evolution of a “macroscopic” coordinate under the influence of coupling to a large number of “intrinsic” degrees of freedom. The equation contains integral operators which lead to energy dissipation and diffusion and reduces to a transport equation of the Fokker-Planck type if the form factors in the integrands are treated in appropriate (harmonic) approximations. The stationary solution of the partial integro-differential equation is obtained numerically for scattering by a conservative potential and by a dissipative and diffusive scattering centre in one spatial dimension.
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Cassing, W., Friedrich, H. On the quantum mechanical description of scattering by a dissipative and diffusive scattering centre. Z Physik A 291, 339–346 (1979). https://doi.org/10.1007/BF01408384
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DOI: https://doi.org/10.1007/BF01408384