Physics / advanced
Scattering amplitudes from quantum potentials
Connect scattering states and observable cross sections through partial waves, integral equations, resonances, and low-energy universality.
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Module 01 advanced
Scattering amplitudes from quantum potentials
Connect scattering states and observable cross sections through partial waves, integral equations, resonances, and low-energy universality.
- 01
Asymptotic scattering states and flux
Normalize incident and outgoing waves so that a scattering amplitude predicts a measurable event rate.
35 min - 02
Partial-wave phase shifts
Resolve central-potential scattering into angular momentum channels and extract phase shifts from radial matching.
35 min - 03
Optical theorem in potential scattering
Derive the forward-amplitude constraint from elastic partial waves and diagnose perturbative apparent violations.
35 min - 04
Born approximation and Fourier potentials
Compute weak-potential amplitudes with an explicit Fourier convention and identify when repeated scattering cannot be neglected.
35 min - 05
Lippmann–Schwinger resolvent equation
Encode outgoing boundary conditions in the free resolvent and distinguish an exact integral equation from its Born iteration.
35 min - 06
S-matrix unitarity and eigenphases
Normalize open channels by flux and distinguish full unitary scattering from loss in a selected elastic channel.
35 min - 07
Breit–Wigner resonances and time delay
Connect an isolated scattering pole to phase motion, width and a wave-packet delay without confusing delay with lifetime.
35 min - 08
Scattering length and effective range
Extract low-energy s-wave parameters with explicit sign conventions and a controlled threshold expansion.
35 min - 09
Bound states as scattering poles
Continue amplitudes into complex momentum and separate normalizable bound states from virtual states and resonances.
35 min - 10
Identical-particle scattering symmetrization
Add direct and exchange amplitudes before squaring and count indistinguishable final pairs once.
35 min