UNIT 1
Scattering
Notes by C. Hartnett and K. Yeter
Scattering is such an important phenomenon that is used in high energy physics
to understand the forces of the nature and the properties of the materials. In
general, there are two types of scattering us
UNIT 5
Time-dependent
perturbation theory
Notes by S. Kyle, A. Sunghoon, and T. Weisong
Introduction and Method
In the former chapter, we talked about the Time-independent Perturbation
Theory. In this chapter, we will work on a more complicated problem, t
UNIT 4
Fine and hyperne
structure of the hydrogen
atom
Notes by N. Sirica and R. Van Wesep
Previously, we solved the time-independent Schdinger equation for the Hydroo
gen atom, described by the Hamiltonian
p2
e2
(1)
2m
r
Where e is the electrons charge i
UNIT 3
Stationary perturbation
theory
Notes by L. Poudel, T. Papatheodore, and Y. Song
The Method
Perturbation theory applies to systems whose Hamiltonians may be expressed
in the form
H = H0 + W.
(1)
H0 is called the unperturbed Hamiltonian and it is ass
UNIT 2
Angular momentum
Notes by J. Mazer, A. Holt, M. Rezaee
Angular Momentum
The angular momentum classically is given as:
L=rp
(1)
When we write this as an operator is it shown that the components satisfy the
communtation relation:
[Lx , Ly ] = i Lz
(2
PHYSICS 522 - SPRING 2011
Final Exam
Problem 1
The magnetic moment of a nucleon is
n =
e
(g L + gS S )
2mn c
where mn is its mass. For a proton, g = 1 and gS = 5.587, and for a neutron, g = 0 and
gS = 3.826.
Let J = L + S be the total angular momentum. De
PHYSICS 522 - SPRING 2011
Midterm Exam II - Solutions
Problem 1
1
3
(a) There are 2 4 = 8 states in this system, |m1 m2 , with m1 = 2 , m2 = 2 , 1 .
2
Let S = S1 + S2 be the total spin. Then
a
2
2
H = [S 2 S1 S2 ]
2
Evidently, the eigenstates are |SM with
PHYSICS 522 - SPRING 2011
Midterm Exam II
Problem 1
Consider a system consisting of a spin 1/2 particle and a spin 3/2 particle governed by the
Hamiltonian
H = aS1 S2
where S1 and S2 are the two spin operators.
(a) Find the energy levels of the system and
PHYSICS 522 - SPRING 2011
Midterm Exam I - Solutions
Problem 1
Using
J =
we obtain
JS,r =
i
+ c.c.
2m
i
eikr
|f |2
2m
r
eikr
r
+ c.c. =
k1 2
|f |
m r2
i 1 f
f
+ c.c.
2m r3
1
f
i
f
+ c.c.
=
2m r3 sin
JS, =
JS,
Total current:
IS =
dr2 JS,r
r=R
=
dR2
k1
PHYSICS 522 - SPRING 2011
Midterm Exam I
Problem 1
An incoming beam of particles represented by the wavefunction
in (r) = eikz
gives rise to a scattered (outgoing) wave represented by
S (r) = f (, )
eikr
r
Find the probability current JS corresponding to