1
The Quantum Anharmonic Oscillator
Perturbation theory based on Feynman diagrams can be used to calculate observables in Quantum Electrodynamics, like the anomalous magnetic moment of the electron, and the predictions agree with experiment
with impressiv
1
Interaction of Quantum Fields with Classical Sources
A source is a given external function on spacetime t, x that can couple to a dynamical variable like a
quantum eld. Sources are fundamental in the functional and path integral formulations of eld theo
PHY 510
Advanced Quantum Mechanics
Fall 2013
Homework Assignment 1
Please format your submission as a single PDF le according to the instructions in the syllabus
and submit it on UBlearns before 11:59 pm on Sunday, September 8.
Problem 1: Relativistic Par
Topic 6
Applications of Quantum Electrodynamics
Lecture 34
Photon Attenuation in Matter
NIST XCOM: Photon Cross Sections Database A web database is provided which can be used to calculate
photon cross sections for scattering, photoelectric absorption and
Topic 6
Applications of Quantum Electrodynamics
Lecture 35
Relativistic Coulomb Scattering
E. Rutherford, The Scattering of and Particles by Matter and the Structure of the Atom, Phil. Mag.
21, (1911) Helge Kragh, Rutherford, Radioactivity, and the Atomic
Topic 6
Applications of Quantum Electrodynamics
Lecture 36
The Electron Vertex Function
PHY 510
1
11/18/2013
Topic 6
newton.jpg
Applications of Quantum Electrodynamics
boltzmann.jpg
Lecture 36
dirac.jpg
J. Schwinger, On Quantum-Electrodynamics and the Mag
Topic 7
Broken Symmetry and Phase Transitions
Lecture 37
Mean Field Theory
In previous topics, the microscopic atomic degrees of freedom, electrons, ions, and photons, were described
by the fundamental equations of quantum electrodynamics. The elementary
Topic 6
Applications of Quantum Electrodynamics
Lecture 33
Electron-Positron Annihilation using Spinor Technology
The annihilation amplitude in the high-energy limit me 0 and m 0 is
e2
M = 2 [(p ) u(p)] [(k)v(k )]
v
u
q
Use explicit right- and left-handed
Topic 5
Interactions and Feynman Diagrams
Lecture 30
Ground State Energy of the Interacting Electron Gas
This important topic is discussed in Altland-Simons 5.2. The basic concepts and methods also apply to the
degenerate electron gas in White dwarf stars
Quiz 41
Dec 4, 2013
H=
k nk
k
Quiz 40
g
Ld
c c ck +q ck .
k+q k
k,k ,q
Dec 2, 2013
energy, temperature and chemical potential. Using the product wavefunctions of 2, 3 and 4 identical particles
as examples, explain the dierence between Bose-Einstein and Ma
PHY 510
Advanced Quantum Mechanics
Midterm Exam
Monday, October 21
Name:
UB ID:
This is a closed-book/computer exam.
One textbook and one binder with personal notes/printouts is allowed.
Try to make your answers brief and clear.
The page provided with
Topic 7
Broken Symmetry and Phase Transitions
Lecture 41
Meissner Eect in a Superconductor
Setting the superuid density to a constant value ns and performing the Gaussian functional integration
over the phase of the condensate gives the eective action for
Topic 7
Broken Symmetry and Phase Transitions
Lecture 40
Spontaneous Symmetry Breaking and Nambu-Goldstone Bosons
Yoichiro Nambu 1921 Nobel Laureate in Physics in 2008, with
Makoto Kobayashi and Toshihide Maskawa.
In 1960, Nambu and Jona-Lasinio proposed
Topic 6
Applications of Quantum Electrodynamics
Lecture 32
Production of Quark-Antiquark Pairs
PHY 510
1
11/8/2013
Topic 6
Applications of Quantum Electrodynamics
Lecture 32
Particle Data Group: cross section plots Cross Section Plots.
International Linea
Topic 7
Broken Symmetry and Phase Transitions
Lecture 39
Superconductivity
Heike Kamerlingh Onnes 1853 1926
Nobel Laureate in Physics in 1913 for his investigations on the properties
of matter at low temperatures which led, inter alia to the production of
Topic 7
Broken Symmetry and Phase Transitions
Lecture 38
Bose-Einstein Condensation and Superuidity
Satyendranath Bose 18941974
He undertook important work in quantum theory, in particular on Plancks
black body radiation law. His work was enthusiastically
Topic 5
Interactions and Feynman Diagrams
Lecture 25
Interacting Fields and Feynman Diagrams
Chapter 4 of Peskin-Schroeder develops the Feynman diagram method for the 4 scalar eld theory and for
Quantumelectrodynamics. The 4 theory for a real scalar eld
1
PHY 510
Advanced Quantum Mechanics
Fall 2013
Homework Assignment 6
Please format your submission as a single PDF le according to the instructions in the syllabus
and submit it on UBlearns before 11:59 pm on Sunday, October 13.
Problem 1: Spinor Products:
PHY 510
Advanced Quantum Mechanics
Fall 2013
Homework Assignment 5
Please format your submission as a single PDF le according to the instructions in the syllabus
and submit it on UBlearns before 11:59 pm on Sunday, October 6.
Problem 1: Lorentz group: Pes
PHY 510
Advanced Quantum Mechanics
Fall 2013
Homework Assignment 7
Please format your submission as a single PDF le according to the instructions in the syllabus
and submit it on UBlearns before 11:59 pm on Sunday, October 27.
Problem 1: The Lagrangian fo
PHY 510
Advanced Quantum Mechanics
Fall 2013
Homework Assignment 8
Please format your submission as a single PDF le according to the instructions in the syllabus
and submit it on UBlearns before 11:59 pm on Sunday, November 3.
Problem 1: Decay of a Scalar
PHY 510
Advanced Quantum Mechanics
Fall 2013
Homework Assignment 9
Please format your submission as a single PDF le according to the instructions in the syllabus
and submit it on UBlearns before 11:59 pm on Sunday, November 10.
Problem 1: Solitons in Poly
PHY 510
Advanced Quantum Mechanics
Fall 2013
Homework Assignment 10
Please format your submission as a single PDF le according to the instructions in the syllabus
and submit it on UBlearns before 11:59 pm on Sunday, December 8.
Problem 1: Coulomb scatteri
PHY 510
Advanced Quantum Mechanics
Fall 2013
Homework Assignment 4
Please format your submission as a single PDF le according to the instructions in the syllabus
and submit it on UBlearns before 11:59 pm on Sunday, September 29.
Problem 1: Show that the c
PHY 510
Advanced Quantum Mechanics
Fall 2013
Homework Assignment 3
Please format your submission as a single PDF le according to the instructions in the syllabus
and submit it on UBlearns before 11:59 pm on Sunday, September 22.
Problem 1: Feynman Diagram
Topic 5
Interactions and Feynman Diagrams
Lecture 29
SNEG: Mathematica Package for Solid State Physics
R. Zitko, SNEG Mathematica package for symbolic calculations with second-quantization-operator expressions, Comput. Phys. Commun. 182, 22592264 (2011) a
Topic 4
Path Integral Quantization
Lecture 24
Bosonization and Fermionization
Fermions in 2-Dimensional Spacetime
The Lagrangian density for QED in 4-dimensional spacetime is
LQED = LDirac + Lint + LMaxwell = (x) [i m] (x) e(x) (x)A(x) 1 F F ,
4
where (x)
Topic 5
Interactions and Feynman Diagrams
Lecture 28
Basic Formulas for Cross Sections and Decay Rates
The Scattering cross section is dened by Peskin-Schroeder on page 100 by the formula
Number of scattering events of a given type
.
A A B B A
where A is
Topic 5
Interactions and Feynman Diagrams
Lecture 26
Ginzburg-Landau Theory of Type II Superconductors
This interesting application of quantum eld theory is reviewed by B. Rosenstein and D. Li, Ginzburg-Landau
theory of type II superconductors in magnetic