1 answer

Statistical Mechanics - Microcanonical ensemble problem from Statistical Mechanics: Theory and Molecular Simulation by Mark Tuckerman...

Question:

of N identical particles 3.1. Consider the standard Hamiltonian for a system of N identical part H = C P +U(r...,EN). a. Show

Statistical Mechanics - Microcanonical ensemble problem from Statistical Mechanics: Theory and Molecular Simulation by Mark Tuckerman

of N identical particles 3.1. Consider the standard Hamiltonian for a system of N identical part H = C P +U(r...,EN). a. Show that the microcanonical partition function can be expressed in the form N(N,V, E) – My [ae ſaxpo( -E) Nr 8(Ur....IN) - E+E'), Jor which provides a way to separate the kinetic and potential contributions to the partition function. Based on the result of part a, show that the partition function can, there- fore, be expressed as 3/27 (N, V, E) = dNr E-U(r.....In)3N/2-10 (E-U (11,...,IN)), JD(V) where 0(x) is the Heaviside step function.

Answers

(a) The phare space volume for a system of wideutical particle is, (30) dr = dig, de ... dow dp .... den 1. NI LEN N! LEN N lbut we have detta function property SCx-y)- Sdz 8(x-2) scz -y) - = -18CM,VE) - M S de So de se -=) $(#- (-26 -2] + =)) - Mycncm, v. )= mon comme s del Sud Slaget_ #) (sCuca-- .)– E+ ) dv DCU Let transform into an dimensional spherical co-ordinatesSN-I 3N- 0 DCV) 31- due S do slucz ---- ) - E+E) - ms (Gomom s de (23* i Sverige Sci s(uck -- a)=E+) for long w, take ( due

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