Qualifier Prep Week 2
General Principles in Quantum Mechanics
You must be able to calculate the
following without taking time to think
Probabilities
Expectation Values
Time-Dependent Wavefunctions
Basic Statistical Physics
Variational Ground-state Energy
Qualifier Prep Week 11
Newtonian Mechanics
Write down the right equation.
Conservation of Energy
Conservation of momentum
F = ma
Conservation of Angular Momentum ( = 0)
A person should be comfortable with ALL of
the terms that are most likely to appea
Qualifier Prep Week 8
Modern Topics
Pick Your Pony (a.k.a. your topics)
As previously mentioned
For the modern exam, you must be able to do
problems in at least 2 of the following topic areas:
Astrophysics
Nuclear Physics
High Energy (Particle) Physics
Qualifier Prep Week 4
Spin
Spin
Spin Operators (S2, Sz, S1S2, S)
Rewriting in terms of a different basis
Pauli Spin Matrices
Different Representations
NOTE: The same stuff applies for problems
dealing with orbital angular momentum.
Spin Operators and
Studying for the ISU Physics
Written Qualifying Exam
Note: This is NOT the same as just Studying Physics
Study the right things!
This exam directly tests
This exam indirectly tests.
Your ability to complete qualifier questions
in a limited amount of time
Qualifier Prep Week 5
Relativity
and for Lorentz Transformations
1
2
1
v
c
For a Lorentz Transformation, and are
unit-less values dependent on v which is
defined as the velocity of the primed system
with respect to the unprimed system.
Lorentz Transform
Qualifier Prep Week 10
Perturbation Theory
When values are small
Its a perturbation! (See Griffiths QM Chap 6)
H H H
o
The Hamiltonian is made up of an
unperturbed portion (H0) and a perturbed
portion (H)
1st Order Non-degenerate PT
The energy correct
Qualifier Prep Week 7
E&M Part I
The Fundamental Equations
E
0
B 0
B
E
t
E
B 0 j 0
t
F q E v B
B A
A
E V
t
Maxwells Equations
Gauss ' Law :
qenc
E E dA
0
0
No magnetic monopoles :
B 0 B dA 0
Faraday ' s Law :
B
B
E
mf E dl
t
t
Maxwell
Qualifier Prep Week 2
The Schrodinger Equation
for Various Potentials
Potentials that you need to know
One Dimensional Potentials
Infinite Square Well
Ring
Delta Function
Barrier
Finite Square Well
Harmonic Oscillator
3 Dimensional Potentials
Box
Infini
Qualifier Prep Week 1
Essential Math Methods and Tricks
Differential Equations
Important for all topics
Lagrangian Mechanics
Newtonian Mechanics
Electricity and Magnetism
Quantum Mechanics
Writing, Solving, and Interpreting Differential
Equations is
Qualifier Prep Week 3
Lagrangian Mechanics
Lagrangian Mechanics
Choosing a Coordinate System
Point Objects vs. Continuous Objects
Moments of Inertia
Equations of Motion
Calculating the Normal Modes
Constants of the Motion
Hamiltons Equations
Review: App