Scattering

Question 1

Introduction to scattering theory: differential cross section, solutions of the free Schroedinger equation, scattering amplitude

Question 2

Scattering phase shifts: definition, relation to solutions of the free Schroedinger
equation, example of hard spheres, Levingston theorem

Question 3

Square well potential: expression for the s-wave phase shifts, bound state
conditions

Question 4

Analytical structure of the S matrix: regular solution, Jost functions,
bound states and resonances

Question 5

Resolvent operators, Green’s functions, Lippmann-Schwinger equation,
scattering amplitude in terms of G+

Question 6

Born series, analytical properties of S matrix as a function of λ

Question 7

Time dependent scattering theory: asymptotic states, proof of existence
of interacting state given asymptotes

Question 8

Moeller operators, their ranges, scattering operator and its momentum
space matrix elements

Question 9

Relation between Moeller operators and resolvents, definition of T matrix

Question 10

On-shell T matrix and scattering amplitudes, optical theorem

Question 11

Rotational invariance in scattering problems, and partial wave expansions
of S,T and scattering amplitude

Question 12

Low energy scattering and the effective range expansion