Scattering Operators and Unitarity
The operator formulation separates the exact scattering problem from a particular approximation to its solution. The Lippmann–Schwinger equation fixes the boundary condition through the resolvent; the transition operator encodes amplitudes, while unitarity constrains their observable consequences. The Born series and its first approximation belong here as scattering-specific uses of perturbation theory.
Helpful background. Use linear operators and Green functions; consult the general approximation volume for the logic of controlled expansions.
Enter this chapter
Section titled “Enter this chapter”- S-Matrix
- T-Matrix
- Lippmann-Schwinger Equation
- Green Function for Scattering
- Born Series
- First Born Approximation
- Validity of the Born Approximation
- Optical Theorem
- Unitarity
Use Scattering Theory to choose another chapter. General perturbative, variational, and semiclassical strategies are collected in Approximation and Semiclassical Methods.