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momentum, m the mass, and ct e modified Bessel functions Ky(z): = 6th e e-zcosht cost

momentum, m the mass, and ct e modified Bessel functions Ky(z): = 6th e e-zcosht cost

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Determine the probability distribution function in the phase space for a relativistic particle in a volume V and with energy ε(p) = √√√/m²c²+p²c², where p is the ab- solute value of the momentum, m the mass, and c the speed of light. Give the final result in terms of the modified Bessel functions r+∞ Ky (z) = ™ (v-1)! 2 -zcosht e cosh (vt) dt Ky(z) ~ Check what happens in the limit ² →0. mc² kT z<< 1,v> 0.
Transcribed Image Text:Determine the probability distribution function in the phase space for a relativistic particle in a volume V and with energy ε(p) = √√√/m²c²+p²c², where p is the ab- solute value of the momentum, m the mass, and c the speed of light. Give the final result in terms of the modified Bessel functions r+∞ Ky (z) = ™ (v-1)! 2 -zcosht e cosh (vt) dt Ky(z) ~ Check what happens in the limit ² →0. mc² kT z<< 1,v> 0.
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