Scattering Theory 29:276
Scattering Theory
29:276
Fall 2004
Class Information
- Room: 63, Van Allen Hall
- Time: 9:30-10:20AM
- Days: Monday, Wednesday, Friday
- Text: Scattering Theory of Wave and Particles,
R. Newton, Dover, 2002
Instructor Information
- Instructor: Wayne Polyzou
- Office: 306 Van Allen Hall
- E-mail: polyzou@uiowa.edu
- Phone: 319-335-1856
General Information
Scattering theory is the most important tool for learning about
the structure and interactions of atomic, nuclear, and
sub-nuclear systems. I will start by covering basic aspects of
scattering theory. The first few lectures will develop time-dependent
scattering theory. This will be used to derive familiar expressions
from time-independent scattering theory. In this development I will
discuss the definition of the scattering cross section and how to
apply scattering theory to real experimental situations, such as
partially polarized beams of projectiles. I will discuss the role of
symmetries in scattering theory. While most of the development will
be on scattering theory in non-relativistic quantum mechanics, I will
also discuss the relationship to classical scattering, relativistic
scattering, and scattering with long-range interactions.
Later in the semester I will discuss the two and three-body
scattering in detail. Of particular interest in the two-body
problem are analytic properties of scattering amplitudes and their
relation to bound states and the inverse scattering problem,
scattering equivalences and the interpretation of observables. I will
also discuss computational methods for solving scattering problems. For
the three and many-body problem I will discuss the Faddeev equation
and its many-body generalizations.
A portion of the class may be devoted to specific areas of student
interest. Some potential topics for projects are scattering with
confining interactions, radon transforms and imaging, scattering of
black holes, scattering and particle production, and moment-methods.
Homework will be assigned on a regular basis. In addition to
homework, each student will be required to prepare a paper on a topic
of interest and to present a short talk on her/his chosen topic at the
end of the semester. The final grade will be based on the homework,
the final paper, and the oral presentation.
I plan to cover a number of topics. It is impossible to find all
of them all in a single text; and many only appear in research papers.
I have chosen the text by Newton because it is a good comprehensive
text, a good reference, and it is available in an inexpensive
paperback edition from Dover. I will post notes on all of
the material that I cover in lectures.
Office hours: TBA.
Course website: http://www.physics.uiowa.edu/~wpolyzou/scattering/
Lecture Notes
Supplementary References (Books)
- Scattering Theory in Quantum Mechanics,
W. Amrein, J. Jauch, K. Sinah, W. A. Benjamin, (1977)
- Mathematical Theory of Quantum Fields, H. Araki, Oxford (1999)
- Mathematical Scattering Theory, H. Baumgartel and M. Wollenberg,
Birkhauser, (1983)
- Mathematical Aspects of the Three-Body Problem in the
Quantum Scattering Theory , L. D. Faddeev,
Israel Program of Scientific Translations, (1965)
- The Quantum Mechanical Few-Body Problem, W. Gloeckle, Springer,
(1983)
- Collision Theory, by M. L. Goldberger and K. M. Watson,
Wiley (1964)
- Local Quantum Physics, R. Haag, Springer (1992)
- Perturbation Theory for Linear Opeartors, T. Kato, Springer
(1966)
- Scattering Theory by the Enss Method , P. Perry, Harwood (1983)
- Scattering Theory, M. Reed and B. Simon, AP (1979)
- The Quantum Theory of Scattering, L. Rodberg and R. Thaler,
AP (1967)
- Quantum Scattering Theory, M. Ross, Indiana University Press,
(1963)
- The Quantum Mechanical Three Body Problem,
E. Schmidt and H. Ziegelmann, Pergamon (1974)
- Scattering Theory, J. R. Taylor, Wiley, (1972)
- Classical Dynamical Systems, W. Thirring, Springer (1978)
- Topics in Several Particle Dynamics, K. Watson and J. Nuttall,
Holden Day, (1967)
- Quantum Theory of Scattering, T-Y Wu and T. Ohmura,
Prentice Hall (1962)
Supplementary References (Papers)
- N. Andersson, B.P. Jensen,
Scattering by Black Holes ,
arxiv:gr-qc/0011025
- Gy. Bencze and E. F. Redish,
General algebraic theory of identical particle scattering ,
J. Math. Phys. 19,1909(1978)
- C. Chandler and A. Gibson,
The General Invariance Principle ,
Indiana University Math J. 25,443(1976)
- F. Coester and W.N.Polyzou,
Relativistic Quantum Mechanics of Particles with Direct Interactions,
Phys. Rev. D26, 1348(1982).
- R. F. Dashen, J. B. Healy, I. J. Muzinich,
Potential Scattering with Confined Channels, Ann.
Physics, 102,1,(1976)
- J. D. Dollard, Asymptotic Convergence and the Coulomb Interaction,
J. Math. Phys., 5,729(19664)
- V. Glaser, H. Lehamnn, W. Zimmermann
Field Operators and Retarded Functions,
Nuovo Cimento 6,1122(1957)
- W. Gloeckle, H. Witala, D. Huber, H. Kamada, J. Golak,
The Three Nucleon Continuum: Achievements, Challenges and Applications,
Phys. Rpt. 274,107(1996)
- R. Haag,
Quantum Field Theories with Composite Particles and
Asymptotic Completeness, Phys. Rev. 112,669(1958)
- R. Haag, H. Araki,
Collision Cross Sections in Terms of Local Observables,
Comm. Math. Phys., 4,77(1967)
- W. Hunziker,
The S-Matrix in Classical Mechanics,
Comm. Math. Phys. 8,282(1968)
- T. Kato, Wave Operators and Unitary Equivalence,
Pacific J. Math., 15,171(1965)
- B. D. Keister W. Polyzou,
Relativistic Hamiltonian Dynamics in Nuclear and Particle Physics,
Advances in Nuclear Physics Volume 20, Ed. J. W. Negele and
E.W. Vogt, Plenum Press (1991)
- B. M. Kessler, G. L. Payne, W. N. Polyzou,
Scattering Calculations with Wavelets,
Few-Body Systems, 31,1(2003),
nucl-th/0211016.
- R. Maj and S. Mrowczynski,Inaccurate use of Asymptotic Formulas,
arxiv:physics/0401063
- W.N.Polyzou and E.F.Redish,
Unified Connected Theory of Few-Body Reaction Mechanisms in
N-body Scattering Theory, Ann. Phys, 119,1(1979)
- W.N.Polyzou, W.H.Klink, and G.L.Payne,
A Noncompact Kernel Integral Equation for
Three-Body Scattering II. Derivation of Boundary Conditions,
Phys. Rev. C30, 1140(1984).
- W. N. Polyzou,
Cluster Properties in Relativistic Quantum Mechanics of N-Particle Systems,
J. Math. Phys. 43,6024(2002), nucl-th/0201013
- W. N. Polyzou,
Left Coset Invariance and Relativistic Invariance,
Few-Body Systems 27,57(1999)
- William P. Reinhardt,
Fredholm Calculations of Electron
Atom Scattering Amplitudes using L2 Basis States,
Computer Physics Communications 6,303(1973)
- D. Ruelle,
On the Asymptotic Condition in Quantum Field Theory,
Helv. Phys. Acta. 35,34(1962)
- C. Van Winter,
Complex dynamical variables for multiparticle systems
with analytic interactions, I,II, J. Math. Anal. Appl.
47,633(1974); 48,368(1974)
- Jeremy R. Winick and William P. Reinhardt
Moment T-Matrix apporache to e+ - H scattering II, Elastic Scattering
and total cross section at intermediate energies.
Phys. Rev. A 18(1978)925
- M. Reed and B. Simon,
Methods of Mathematical Physics,
Volume IV, Analysis of Operators
p. 183, p 51-61 resonances, p 233 positive eignevalues in the continuum