Elements of Quantum Scattering Theory

  • Brian J. McParland


This chapter provides the elements of quantum scattering theory which shall be used throughout this book. The general scattering problem is reviewed in the context of scattering and time evolution operators and recognises that the observables are the pre- and post-scattering asymptotic states. Quantum perturbation theory is developed with the two linked goals of deriving an expression for the transition probability rate between two quantum states (Fermi’s Golden Rule) and the scattering amplitude and differential cross section (first Born approximation). The Born approximation is derived through the Lippmann–Schwinger equation. The chapter concludes with a phase shift analysis of the scattering problem.


Differential Cross Section Born Approximation Scatter Problem Bear Approximation Phase Shift Analysis 
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Bibliography and Further Reading

  1. Abramowitz M, Stegun IA (eds). Handbook of mathematical functions. New York: Dover Publications; 1972.Google Scholar
  2. Belkic D. Principles of quantum scattering theory. Bristol: Institute of Physics Publishing; 2004.Google Scholar
  3. Churchill RV, Brown JW, Verhey RF. Complex variables and applications. 3rd ed. New York: McGraw-Hill Inc; 1974.Google Scholar
  4. Dyson F. Advanced quantum mechanics. Singapore: World Scientific Publishing; 2007.Google Scholar
  5. Goldberger ML, Watson KM. Collision theory. Mineola: Dover Publications; 2004.Google Scholar
  6. Gribov VN, Nyiri J. Quantum electrodynamics. Cambridge: Cambridge University Press; 2001.Google Scholar
  7. Jackson JD. Classical electrodynamics. 3rd ed. Hoboken: Wiley; 1999.Google Scholar
  8. McParland BJ. Nuclear medicine dosimetry: advanced theoretical principles. Berlin: Springer; 2010.Google Scholar
  9. Messiah A. Quantum mechanics. New York: Wiley.Google Scholar
  10. Sigmund P. Particle penetration and radiation effects. Berlin: Springer; 2008.Google Scholar

Copyright information

© Springer-Verlag London 2014

Authors and Affiliations

  • Brian J. McParland
    • 1
  1. 1.Amersham, BuckinghamshireUK

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