Physics 610B
HW #8
Fall 2007
Due Tuesday, Nov 27, 2007
Problem 8.1 Consider two angular momenta, J1 = 5/2 and J2 = 2. If these are coupled
together (ignoring M for now), what are the possible values for the total J12?
Problem 8.2 For the angular momenta in problem 8.1, explicitly calculate the number of
states in both the uncoupled and coupled bases. Do both bases have the same number of
states?
For the following, use the table of Clebsch-Gordan coefficients I handed out in class
Problem 8.3 Suppose you have two particles, with with (j,m ) = (3/2, 3/2) and the other
with (1, 0). What are the probabilities to find the total state to have total J = 5/2? 3/2? ½?
Problem 8.4. Suppose you have two particles, both with J = 1. They couple together to
form total J = 0. What are the probabilities to find the particles to have, in the uncoupled
basis, to have m = +/- 1? m = 0?
Problem 8.5. Consider a state with orbital angular momentum l = 2 and spin = ½.
Suppose they couple to form total j = 5/2, m = -1/2. Write down the wavefucntion by
coupling together the appropriate spherical harmonics (just use Y2m you don’t need to
write it explicitly in terms of the angles) and spinors, that is, states in the form of a sum
of Y2m χm’ with the appropriate numerical coefficient in front, from the Clebsch-Gordan
table.