Physics 501, Problem Set 4, Due at 12:30 PM, Monday, Mar 10 (No Lates Accepted!)
1) I claimed in class, without proof, that at small k the phase shift for angular momentum quantum number ` behaves
as
` (k) c` k 2`+1
(1)
for some constants c` which depend

Physics 501, Problem Set 3, Due at 12:30 PM, Wednesday, Feb. 12 (No Lates Accepted!)
1) Consider the 2-channel model for a Feshbach resonance discussed in class and in the Duine-Stoof article.
!
2
hm 2 + VT (r)
Vhf
H=
.
2
Vhf
hm 2 + VS (r) + B
(1)
with

Useful Equations
Some of these equations may be useful on the exams or problem sets. Other equations may be provided when
needed.
h2 2
i
h (~r, t) =
+ V (~r) (~r, t)
t
2m
d(x)
= [(0+ ) (0 )](x) + regular part
dx
~2
L
1
2
2
= 2
r
+ 2
r r
r
r
fk (, )

Physics 501, Problem Set 5, Due at 12:30 PM, Monday, Mar 24 (No Lates Accepted!)
1) In class we calculated the 2P transition rate in hydrogen by integrating over all directions of the final velocity of
the emitted photon and summing over both possible pol

Physics 501 Problem Set 1, Due at beginning of class, Wednesday, Jan. 15
1) A scattering amplitude can also be defined for scattering problems in one dimension. In this case we write:
k (x) eikx + fk eikx , (x )
eikx + fk+ eikx , (x ).
(1)
(Here k > 0.)

Physics 501, Problem Set 6 - Official due date: Tuesday, April 7
Automatic extension granted to Monday, April 13 at noon in my office
(No Lates Accepted!)
1) Dirac looked for a Lorentz invariant generalization of the Schroedinger equation that was linear

Physics 501, Problem Set 2, Due in class on Wednesday, January 29 (No Lates Accepted!)
1) Prove the important identity, used for developing scattering theory:
eikr cos =
X
i` (2` + 1)j` (kr)P` (cos ),
(1)
`=0
where the j` are spherical Bessel functions an