Issued Wed Apr 9 Due Fri Apr 18

Required reading: F+H Ch. 10 and 11

1i) F+H 9.26

ii) F+H 9.27

Add: part e) What is the real value of for the K Kbar system? Sketch the probability for this case as well.

Hints: For part a, look back at section (5.7)

For part b, define , and factor out an (irrelevant) overall phase of .

For part c, simplify your answer so that it is manifestly real.

2) F+H 9.29

3a) Use Eqn 10.20 to find out what the units of phase space, are. Show that Eqn 10.29 agrees with that. Then, use Eqn 10.1 to show what the units of must be. So, if you write out , what units must your wave function, , have?

b) Sketch the transition probability factor of Eq 10.13, for T=10^-14 sec, as a function of E (in eV).

c) Does this T satisfy the condition of Eq 10.16, if is a typical atomic value (like 10 eV)?

4) F+H 10.3

Hint: Eq 10.28 tells you the relativistic phase space. (I believe F+H may have taken the non-rel limit) The little v in their answer is velocity

5) F+H 10.13

Dig up an experimental number somewhere for an example of either a) or b), and see how well your crude approximation did.

Hint: You should know typical sizes of atoms and nuclei. I claim that a matrix element (which has units of size here) must be of the same order of magnitude as the object itself. (What other scale could it have?) This might be off by a pretty big factor, but it would probably keep an astrophysicist happy...