8.2: Boltzmann Transport Theory - Physics LibreTexts
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WEBClearly, then, any function of the form \[f(\Br,\Bp,t)=\varphi\big(\Br-\Bv(\Bp)\,t\,,\,\Bp\big)\] will be a solution to the collisionless Boltzmann equation, where \(\Bv(\Bp)={\pz\ve\over\pz\Bp}\). One possible solution would be the Boltzmann distribution, \[f(\Br,\Bp,t)=e^{\mu/\kT} e^{-\Bp^2/2m\kT}\ ,\] which is time-independent 1 .
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