The Universityof Chicago

Department ofPhysics

Course Outlines

Graduate Courses

 

NOTICE

    The Course Outlines and syllabi on this web page represent the best descriptions of some of the graduate courses that are available at this time. The Teaching Activities Committee of the Physics Department expects that these topics be covered, but some deviations may result. You should consult the instructor before choosing to take a course because of a specific topic.

CONTENTS

Physics 316 - Advanced Classical Mechanics (Autumn)
Physics 322 - Advanced Electrodynamics And Optics I (Winter)
Physics 323 - Advanced Electrodynamics And Optics II (Spring)
Physics 330 - Mathematical Methods of Physics I (Autumn)
Physics 331 - Mathematical Methods of Physics II
Physics 341,342  - Quantum Mechanics I and II (Autumn-Winter)
Physics 352 - Statistical Mechanics (Spring)
Physics 361 - Solid State Physics (Autumn)
Physics 363 - Introductory Particle Physics (Spring)
Physics 364 - Introduction to General Relativity (Winter)
Physics 366 - Advanced Solid State Physics/Hard Condensed Matter (Winter)
Physics 367 - Soft Condensed Matter Physics (Winter)
Physics 385 - Advanced Mathematical Methods of Physics (Spring)
Physics 443-444-445 - Quantum Field Theory (Autumn-Spring)
Physics 471 – Introduction to Modern Atomic Physics (Spring)

PHYSICS  322-ADVANCED ELECTRODYNAMICS AND OPTICS I

Level: Classical Electrodynamicsby Jackson

Electromagnetic Fields and RelativisticParticles by Konopinski

The Classical Theory of Fieldsby Landau and Lifschitz

Prerequisite: Physics 330

A. Maxwell's Equations
 

1. Definitions of the vectors E,D, P, and B, M, H.

2. Units

3. Integral and differential formsof Maxwell's Equations

4. Representation of E and B in termsof vector Potential A and
      Scalar Potential f.

5.Gauge Transformations, Lorentz gauge, Coulomb gauge.

6. Wave Equations for E, B, A andq.Retarded integrals

7. Energy, momentum and stress Tensors.Poynting vector, etc.

8. Magnetohydrodynamic limit.

B. Plane Electrodynamic Waves
 

1. Polarization. Form of E andB. Forms of q,A.

2. Hertz vector in vacuum, dielectric,magnetic, dispersive media.

3. Phase and group velocities

4. Conducting medium, dissipation,ground wave.

5. Reflection, refraction, boundaries.

6. MHD waves, cold plasmas, Faradayrotation.

C. Transmission Lines, Wave Guides,Resonant Cavities
 

1. Cylindrical and rectangularboundaries

2. Energy flow, losses.

3. Dielectric waveguides, fiber modes

D. Radiation

 
1. Expansion of retarded integralsfor non-relativistic case

2. Dipole, quadrupole radiation.Near and far fields.

3. Cyclotron radiation, center-fedlinear antenna

4. Thomson scattering. Scatteringby conducting needles

5. Small dielectric spheres.

E. Diffraction.
 

1. Discussion of rigorous solution

2. Huygen's principle and Kirchoff'sintegral

3. Fraunhofer and Fresnel diffraction

4. Rectangular and circular apertures.

5. Fresnel lens, Babinet's principle.

 

PHYSICS  323-ADVANCED ELECTRODYNAMICS AND OPTICS II

Level: Classical Electrodynamicsby Jackson

Electromagnetic Fields and RelativisticParticles by Konopinski

The Classical Theory of Fieldsby Landau and Lifschitz

Prerequisite: Physics 322

A. Review of Special Relativity
 

1. Lorentz transformations of coordinates,field components

2. Four vectors and tensors. Covarianceof Maxwell's equations.

3. Transformation of moving electrically-neutral

current-carrying conductor

4. Covariant Lorentz force.

B. Motion of Charged Particlesin Electromagnetic Fields.
 

1. Equations of motion, propertime, covariant forms.

2. Motion in crossed electric andmagnetic fields

3. Motion in time-varying magneticfield, in plane wave

4. Invariants, of particle motion,guiding center approximation

5. Collisionless plasma equationsas sum over individual particle motions

6. Chew-Goldberger-Low approximation

C. Collisions Between ChargedParticles

 
1. Scattering, energy loss, Coulombcollisions.

2. Equipartition or equilibrationtime for individual particles undergoing       Coulomb collisions with background. Mean free path

3. Scattering of fast particles byatoms

4. Multiple scattering

D. Radiation by Moving and InteractingCharges
 

1. Dipole radiation

2. Lenard-Wiechert potentials

3. Synchrotron radiation

4. Brehmstrahlung

5. Thomson scattering

6. Cerenkov radiation

7. Radiation reaction, radiativedamping

8. Scattering and absorption

9. Line width and level shift ofoscillators

10. Self-energy and self-momentumof charged particle

 

Physics 330: Mathematical Methods of Physics I

Main Text:	Matthews and Walker, Mathematical Methods of Physics
Supplementary Text:	Arfken and Weber, Mathematical Methods for Physicists

1. Complex Analysis
• Analytic functions
• Contour integration
2. Ordinary Differential Equations
• Exact solutions, special functions
• Series solutions
• Approximation methods (WKB, perturbation theory)
3. Linear Algebra
• Vector spaces and matrices
• Infinite-dimensional spaces; Fourier and other transforms
4. Partial Differential Equations and Boundary Value Problems
• General properties
• Green's functions
• Boundary-value problems

Note: This outline is intended as a guide to the most essentialtopics for this course; there is some flexibility in the order and mannerof presentation. In particular, examples of particular applications areleft to the instructor.

 
 

Physics 331/385: Mathematical Methods of Physics II or Advanced Math Methods

Main Text:	Georgi, Lie Algebras in Particle Physics
Supplementary Texts:	Cornwell, Group Theory in Physics: An Introduction
	Tung, Group Theory in Physics
	Sternberg, Group Theory and Physics
	Gilmore, Lie Groups, Lie Algebras, and Some of TheirApplications

1. Basic Concepts of Group Theory
• Finite groups
• Representations and reducibility
2. Lie Groups
• Manifold structure, integration
• Lie algebras
• Global properties; relationship between groups and algebras
• Fundamental and adjoint representations
• SU(2) and its representations
3. Structure of Lie Algebras
• Roots and weights
• Dynkin diagrams
• Classical groups: SO(n), SU(n), Sp(n), Exceptional groups
4. Representations
• Tensor methods
• Clebsch-Gordan decomposition
• Young tableaux
5. Noncompact Groups
• Real and complex forms
• Lorentz group: global structure, discrete subgroups, representations, fermions
• Other noncompact groups

 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

Physics 341, 342 : Quantum Mechanics I,II

Suggested Texts:	R. Shankar, Principles of Quantum Mechanics
	J. Sakurai, Introduction to Quantum Mechanics

1. Fundamentals of Hilbert Space
• Vector spaces and Hilbert spaces
• Dirac notation
• Self-adjoint and Unitary operators and their spectra
• Symmetries and unitary transformations
• Projection operators
2. Simple Quantum Systems and the Relation to Classical Mechanics
• Structure of QM
• Uncertainty Relations
• Two state systems
• One-dimensional problems
• Coherent States
• The classical limit of QM
3. Time Evolution
• Time evolution operator
• Heisenberg equations of motion
• Heisnberg vs. Schrodinger representation
4. Symmetry in Quantum Mechanics
• Angular Momentum and commutation relations
• and spin
• Addition of angular momentum
• Wigner-Eckart theorem
• Identical particle and spin-statistics
5. Interaction with electromagentic fields
• Gauge invariance
• Aharonov-Bohm effect
• Magnetic monopoles
• Stark effect
• Landau levels
• Quantum hall effect
6. Perturbation Methods
• Stationary perturbation theory and applications
• Time dependent perturbation theory
• Fermi's golden rule
• Emission and absorption of radiation
7. Scattering Theory
• General formulation fo scattering
• Cross sections and the scattering amplitude
• Definition of S-matrix and analytic properties
• Scattering of identical particles
8. Path Integral Methods
• Defining sums over paths
• Relation to standard formalism
• Phase space path integrals
• Evaulating gaussian integrals
• Tunneling via instantons
9. Adiabatic approximation and Berry's phase
• Born-Oppenheimer or adiabatic approximation
• Sudden approximation
• Berry's phase and potential
• Global interpretation, examples
10. Measurement theory and decoherence
• Bell's inequalities
• Schrodinger's cat and the problem of collapse of the wave function
• Decoherence, basic idea and simple models
11. Supersymmetric quantum mechanics
• Supersymmetry
• Supersymmetry in quantum mechanics
• Solvable examples
• Supersymmetry and index theory

Comments

The first seven items should be considered the core material, most ofwhich should be covered in the course. There should usually be time tocover some of the remaining four topics (or other topics chosen by theinstructor).

 

 

Physics 363: Particle Physics

Main Text:	Griffiths, Introduction to Elementary Particles
Supplementary Texts:	Halzen and Martin, Quarks and Leptons
	Kane, Modern Elementary Particle Physics
	Perkins, Introduction to High Energy Physics

1. Overview
• Observed particles
• Forces
2. Special Relativity and Classical Field Theory Review
• Spacetime and 4-vectors
• Relativistic kinematics
• Field theory: Lagrangians, electromagnetism, gauge invariance
3. Feynman Diagrams
• Time-dependent perturbation theory
• Feynman rules (at tree level)
• Cross-sections and decay rates
4. Symmetries
• Group theory review
• SU(2) isospin, product representations, SU(3)
• C, P, and T
5. Quantum Electrodynamics
• Spinors and fermions
• Feynman rules
• QED processes, Dirac matrix technology
6. Hadrons and Partons
• Electron-Quark interactions
• Inelastic scattering, partons
• Structure functions
7. Quantum Chromodynamics
• Yang-Mills theory
• Quarks; Feynman rules
• Running couplings
8. Electroweak Theory
• Spontaneous Symmetry Breaking
• Bosonic sector: vector bosons, Higgs
• Fermions, SU(2)
• Generations, CKM matrix, CP violation

 
 

Physics 364: General Relativity

Main Text:	Wald, General Relativity
Supplementary Texts:	Schutz, A First Course in General Relativity
	Weinberg, Gravitation and Cosmology
	Misner, Thorne, and Wheeler, Gravitation
	D'Inverno, Introducing Einstein's Relativity

1. Special Relativity
• Lorentz Transformations
• Spacetime Diagrams
• Vectors and Tensors
• Proper Time
• Physics in Flat Spacetime
2. Manifolds
• Coordinate Systems
• Vectors as Derivatives
• Tensor Transformation Law
• The Metric
• Tensor Densities
3. Curvature
• Covariant Derivatives and Connection Coefficients
• Parallel Transport
• Geodesics
• The Riemann Tensor
• Geodesic Deviation
4. Gravitation
• The Principle of Equivalence
• Physics in Curved Spacetime
• Einstein's Equations
• The Newtonian Limit
5. Weak Fields and Gravitational Radiation
• The Weak-Field Limit
• Linearized Einstein Equations
• Gravitational Waves
6. The Schwarzschild Solution and Black Holes
• Birkhoff's Theorem
• Geodesics of Schwarzschild
• Kruskal Extension
• Penrose Diagrams
• Charged and Rotating Solutions
• Black-Hole Thermodynamics
7. Cosmology
• The Robertson-Walker Metric
• The Friedmann Equations
• Cosmological Redshift
• Inflation

 

Physics 443: Quantum Field Theory I

Main Text:	M. Peskin and D. Schroeder, Introduction to Quantum FieldTheory
Supplementary Texts:	P. Ramond, Field Theory -- a Modern Primer
	C. Itzykson and J. Zuber, Quantum Field Theory
	S. Weinberg, The Quantum Theory of Fields

1. Basic field theory
• Representations of the Poincare group
• Dirac equation
• Noether's theorem
• Canonical quantization
• propagators and causal structure
• Interaction picture
• Time ordered products and Wick's theorem
2. Scattering and Feynman Rules
• LSZ formalism
• Feynman rules for scalar field theory and QED
• Calculation of tree level processes in F⁴and QED
• CPT and spin-statistics
3. One loop effects
• one loop effects in scalar field theory
• Calculation of in QED
• Unitarity and analytic structure of amplitudes

 

 
 

Physics 444: Quantum Field Theory II

Main Text:	M. Peskin and D. Schroeder, Introduction to Quantum FieldTheory
Supplementary Texts:	P. Ramond, Field Theory -- a Modern Primer
	C. Itzykson and J. Zuber, Quantum Field Theory
	S. Weinberg, The Quantum Theory of Fields

1. Path integral formulation of QFT
• Path integrals for boson fields
• Grassman variables and fermion path integrals
• path integral derivation of Feynman rules
• Ward identities in QED
2. Renormalization
• Superficial degree of divergence
• explicit one-loop renormalization of scalar field theory
• Wilson's approach to renormalization
• Fixed points and RG flow
• Callan-Symanzik equation
• Calculation of beta functions and anaomlous dimensions in simple theories
• Critical phenomena
3. Non-Abelian gauge theory
• Construction of gauge invariant actions
• Feynman rules for gauge theories and Fadeev-Popov ghosts
• Calculation of asymptotic freedom in QCD

 

Physics 445: Quantum Field Theory III

Main Text:	M. Peskin and D. Schroeder, Introduction to Quantum FieldTheory
Supplementary Texts:	P. Ramond, Field Theory -- a Modern Primer
	C. Itzykson and J. Zuber, Quantum Field Theory
	S. Weinberg, The Quantum Theory of Fields

1. Effective potentials and symmetry breaking
2. Higgs bosons
3. Formulation of electroweak gauge theory
4. Coupling to quarks and leptons
5. Charged and neutral current processes
6. Properties of W and Z bosons
7. CKM matrix and CP violation
8. Deep inelastic scattering
9. Perturbative QCD
10. Structure functions and Altarelli-Parisi equation

Comments

In most years this course should cover the Standard Model as outlined above. In some years it may cover other advanced topics in QFT such as solitons and instantons, anomalies, large N techniques and lattice gauge theory.
Mel ShochetNormalMelShochet2212001-08-10T01:19:00Z2001-08-10T01:19:00Z2164936Universityof Chicago7111499.2720

 

Physics 471: Introduction to Modern Atomic Physics

 

In this course, a selection of current research topics in the field of atomic physics will be explored. Previous exposure to an atomic physics course is preferred, but not required.

 

There will be no designated text books. However, you may find the following references helpful:

1. Physics of Atoms and Molecules, by B. H. Bransden and C. J. Joachain;
2. Atomic Physics, by D. Budker, D. F. Kimball and D. P. DeMille;
3. Students are expected to read several original papers on each subject.

 

Outline:

1. Nuclear Magnetic Resonance
• Two-level quantum system
• Bloch vector
• Rabi oscillation
2. The Hydrogen Atom

·       Theory: Bohr-Dirac-Schwinger

·       Laser spectroscopy on the 1S-2S transition

·       Positronium, muonium, and anti-hydrogen

3. Trapping and Cooling

·       Ions: Paul trap and Penning trap

·       Neutral atoms: magneto-optical trap and optical dipole trap

4. Atomic Clocks
• Cesium microwave clocks: beam and fountain
• Optical clocks
5. The Fine Structure Constant

·       Fine structure of hydrogen and helium atom

·       The anomalous magnetic moment of electron

·       The constancy of the constant

6. Probing Atomic Nuclei
• Nuclear moment effects
• Nuclear size effects
• Spectroscopy of rare isotopes
7. Fundamental Symmetries in Atoms
• Parity violation
• Time reversal invariance: atomic EDM
• Lorentz invariance
8. Quantum Degenerate Atomic Gases
• Bose-Einstein condensate
• Fermionic degenerate system
9. Quantum information

·       Quantum entanglement

·       Encryption and computation