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A quantum-mechanical Boltzmann equation for one-particle Γs-distribution functions

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  • Prugovečki, Eduard

Abstract

A unified derivation of the classical and quantum Boltzmann equation for the one-particle Γ and Γs distribution functions, respectively, is presented. The starting point is a Boltzmann-like equation for density operators in B2(Γ). In the context of classical mechanics this equation turns into the Boltzmann equation once it is supplanted by the assumption of small spatial inhomogeneity of the Γ-distribution function. Under the same assumption, and after replacing certain δ-like functions with δ-functions, the same procedure yields (for a certain range of values for the instrument characteristic s) a Boltzmann equation for the Γ distribution function. In this last equation a point-target differential cross-section σs appears. The relation of σs to the conventional quantum-mechanical differential cross-section σ is discussed.

Suggested Citation

  • Prugovečki, Eduard, 1978. "A quantum-mechanical Boltzmann equation for one-particle Γs-distribution functions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 91(1), pages 229-248.
    • Handle: RePEc:eee:phsmap:v:91:y:1978:i:1:p:229-248
    DOI: 10.1016/0378-4371(78)90069-9
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    References listed on IDEAS

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    1. Twareque Ali, S. & Prugovečki, E., 1977. "Classical and quantum statistical mechanics in a common Liouville space," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 89(3), pages 501-521.
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    1. Prugovečki, Eduard, 1978. "A unified treatment of dynamics and scattering in classical and quantum statistical mechanics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 91(1), pages 202-228.

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