Recent content by Clara Chung

I am not sure where does the dy term, phi^2 and phi^4 terms come from. I guess there are dx and dy because we have to account for the nearest neighbour pairs in the x and y axis? I guess there is a phi^2 term because 2q_a*q_b=(q_a-q_b)^2-q_a^2-q_b^2, the term q_a^2-q_b^2? How about the phi^4 term?

In 8a) I don't understand the question, does spin = 1/2 mean the magnitude of the spin or the z-component of the spin is 1/2? Can the electrons possesses be any of the spin=1/2 or -1/2? Are the electrons distinguishable?

Attempt: P_1 (initial pressure on the left section) P_2(initial pressure on the right section) T_f, P_f (final pressure for both sections) P_1 (V/3) = N/2 k (3T/2) P_2 (2V/3) = N/2 k (T/2) P_f V/2 = N/2 k T_f Resulting in 4 unknowns and 3 equations... Not enough to find T_f...

He didn't give me the answer. However he said my approach is right and the reason why we can handle N as if it were a deterministic variable is that we are always interested in the thermodynamic limit, where all variables, including N, take a well-defined value. I think the question also assume...

Thank you for your help.. This appears in an exam of an introductory course on atomic physics... I guess I will leave it...

How to know whether they have the same size? :(

If only L=7,8 are approximately degenerate... There are still many levels that can be mixed... Like l=7, ml=0,1,2,3,4,5,6,7 with l=8, ml=1,2,3,4,5,6,7...??

Yes, it should be zero :)

For n=7 and n=8 there will be n^2 eigenfunction... if the states that will be mix are the states that satisfy the selection rules... i.e. delta l=+-1 and delta m=0, there will be so many... not only the two eigenstates in the hydrogen atom...?

I have attached the two pages in my notes and I have the following question. 1. Where have the n_t*l gone in 9.9? (According to 9.5 why do they disappear?) 2. Why J_s=sigma_tot J_i? The dimension of flux is per m^2 and sigma is per area too, the dimension is not right...

For e ii) The answer is Why are there only 4 sublevels? We haven't learned about degenerate perturbation theory, the only thing mention in lecture is which I don't understand so I only memorize the good eigenfunctions for n=2. Could you explain why there are still only 4 sublevels for n=7 and 8?

Attempt:

c) Z = 1 + e^(-2bE) + e^(-bE) Bosons: State 1: Two atoms in well 1 probability: 1/Z State 2: Two atoms in well 2 p=e^(-2bE)/Z State 3: Each well is occupied by 1 atom P=e^(-bE)/Z P_1(1)=P_2(1)=e^(-bE)/Z P_1(2)= 1/Z P_2(2)= e^(-2bE)/Z Fermions: State 1...

b) Consider P_j(n) as a macrostate of the system, Bosons: State 1: Two atoms in well 1 State 2: Two atoms in well 2 State 3: Each well is occupied by 1 atom Can I use the apriori principle that each microstate is equally possible? In this case all states will have a probability of 1/3...

b) Consider P_j(n) as a macrostate of the system, Bosons: P_1(1) = P_2(1) = 1/2*1/2=1/4 ,P_1(2)=P_2(2)=1/2*1/2=1/4 Fermions: P_1(1)=P_2(1)=1 (Pauli exclusion principle), P_1(2)=P_2(2)=0 Different species: P_1(1)=P_2(1) = 2*1/2*1/2=1/2 (because there are two microstates with corresponding to...