Issued Wed., Dec 3. (This is NOT to be handed in, but do it - it's a guide for studying chapter 8)

The final will be held on Sat, Dec. 13, 3:30-6:30 in our regular classroom. The final may cover any material from the entire semester, but will focus on material since the 2nd exam, i.e. Gas. Ch 7-12. (There will be something regarding many-particle systems)

Required reading for this week: Ch. 8

There are HINTS for this homework.
1 i) Gas 8-6

ii) Repeat, but if the particles are identical bosons instead of fermions.

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

2) Two distinguishable particles of equal mass m (e.g. proton and neutron) are attached to each other by a massless rope, length L. (As long as they are less than L apart, they feel no force at all, but it is impossible for them to get farther apart than L.) The rope is indestructable. The particles are otherwise non-interacting. (Work only in 1 dimension!)

a) What is the system's minimum energy? Also, write down a complete two-body ground state wave function, including time dependence.

b) Repeat part a, if the 2 particles ar now identical (spin "up") electrons.

(Does your wave function vanish if x1=x2? Should it? Why?)

c) Repeat again, if the 2 particles are identical hydrogen atoms (spin 0).

How would your above answers change if the systems are given an additional overall center of mass momentum, P?

3) Put 2 identical 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 (e.g. proton and neutron).