Determine the probability distribution function in the phase space for a relativistic particle in a volume V and with energy &(p) = √m²c + 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 -zcosht cosh(vt) dt Kv (2) = (v-1)! Ky(z) = ¹¹ (1) Check what happens in the limit - 2 z<1.v>0.

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Problem 7.27.
Determine the probability distribution function in the phase space for a relativistic
particle in a volume V and with energy &(p) = √m² + 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
Kv (z) = f
-zcosht
1)!
Ky(z) = (
Check what happens in the limit →0.
2
V
cosh(vt) dt
z< 1.v>0.
Transcribed Image Text:Problem 7.27. Determine the probability distribution function in the phase space for a relativistic particle in a volume V and with energy &(p) = √m² + 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 Kv (z) = f -zcosht 1)! Ky(z) = ( Check what happens in the limit →0. 2 V cosh(vt) dt z< 1.v>0.
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