(a) By considering some small numbers N and m, verify that the number of ways (degeneracy (2) of sharing m quanta, each

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A By Considering Some Small Numbers N And M Verify That The Number Of Ways Degeneracy 2 Of Sharing M Quanta Each 1 (41.13 KiB) Viewed 14 times

(a) By considering some small numbers N and m, verify that the number of ways (degeneracy (2) of sharing m quanta, each of energy c, amongst N oscillators g(N, m) = (N+m-1)!/[(N-1)!m!]. is: (b) Enumerate the degeneracy of a system of 4 oscillators and a system of 2 oscillators for up to 5 quanta each. For this and the following section it may be worth writing a short MATLAB script! (c) Consider 3 systems, A, B and C in thermal contact i.e. able to exchange energy with one another. The sytems A and B each consist of 4 oscillators and system C consists of 2 oscillators. What are the most likely ways in which 5 quanta will be shared when the three systems are in equilibrium? Comment on your answer. (d) Two systems containing large numbers (N₁ and N₂) of weakly interacting oscillators are in thermal contact. If the total energy available to be shared amongst the N₁ + N₂ oscillators is fixed at me, obtain an expressions for (m₁), the number of ways in which system 1 has energy mic and system 2 has energy mae where m₁ + m₂ = m. By evaluating the first and second derivatives of 2 w.r.t. m₁, show that the most probably value of my satisfies the relation m₁/N₁-m₂/N₂ and that the sharing of energy between the two systems will be very sharply peaked at this value.