Issued Wed, Nov 6 Due Wed, Nov 13

(Reminder: Exam 2 is Thur, Nov 7, 7:30 PM in Muen E064)

Required reading for this week: Ch. 8

1) Gas. problem # 8-2

2) Gas 8-4

3) i) Gas 8-6

ii) Repeat Gas 8-6, if the particles are identical bosons instead of fermions.

iii) Repeat again, if the particles are distinguishable (eg proton and neutron)

4) Gas. Problem 5. (I found his problem a little hard to understand, so here's MY wording of it:)

Consider 2 distinguishable, equal mass particles in a harmonic oscillator, so .

a) Using coordinates x1 and x2, you can pretty easily solve Hu(x1,x2)=Eu(x1,x2) by setting (and knowing how to solve 1-D harmonic oscillators) Do this to find the resulting energy spectrum for the two particle states.

b) Now switch to center of mass coordinates (Gas. Eq 8-28), and rewrite H in terms of x and X (and p and P). (First find p and P in terms of p1 and p2)

Again, you can pretty easily solve Hu(x,X)=Eu(x,X) (Use separation of variables, you know how to solve 1-D harmonic oscillators) Do this to find the resulting energy spectrum.

c) Discuss/describe the degeneracy of the energy spectrum you found for parts a and b.

5) Put 2 particles into a harmonic oscillator, with one particle in the n-th state, and the other in the n'-th state.

a) Calculate if the particles are identical fermions. (So, they can't be in the same state, i.e. n can't be the same as n'.) As in other problems, you should assume the electrons have the same spin.

b) Repeat part a, but with identical bosons. (For this case, you must also consider the possibility n=n')

c) Repeat part b, with distinguishable particles.