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In classical statistical physics we have the partition function:
Z=Ʃexp(-βEi)
But my book says you can approximate this with an integral over phase space:
Z=1/(ΔxΔp)3 ∫d3rd3p exp(-βE(r,t))
I agree that x and p are continuous variables. But who says that we are allowed to make this kind of discretization and what values are we choose for 1/(ΔxΔp)3 except for them being small?
I think my book is definitely hiding something from me, and using a rather lame argumentation in doing so.
Z=Ʃexp(-βEi)
But my book says you can approximate this with an integral over phase space:
Z=1/(ΔxΔp)3 ∫d3rd3p exp(-βE(r,t))
I agree that x and p are continuous variables. But who says that we are allowed to make this kind of discretization and what values are we choose for 1/(ΔxΔp)3 except for them being small?
I think my book is definitely hiding something from me, and using a rather lame argumentation in doing so.