Quantum Mechanics · Chapter 23

Scattering

Most of what is known about forces between particles was learned by firing one at another and counting what comes out. Cross sections, the scattering amplitude, the integral equation and its Born approximation, Coulomb scattering, the partial waves and phase shifts of a central potential, the optical theorem, and scattering at low energy with its resonances.

\frac{d σ}{d Ω} = ∣ f (θ, ϕ) ∣^{2}

ψ \sim e^{ik z} + f (θ) \frac{e ^{ik r}}{r}

S = I + i T

σ = \int \frac{d σ}{d Ω} d Ω

Lessons

Build the foundation

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07Phase shiftsEach phase shift has a plain meaning: far from the potential, the radial wave of angular momentum $\ell$ is $\sin(kr-\ell\pi/2+\delta_{\ell})$ instead of $\sin(kr-\ell\pi/2)$, shifted by $\delta_{\ell}$.Read lesson →

08The optical theoremParticles scattered out of the beam must be missing from it: behind the target there is a shadow.Read lesson →

09Low-energy scattering and resonancesAt low energy only the s wave scatters, and its phase shift vanishes in proportion to $k$: $\delta_{0}\approx-ka$.Read lesson →

10Chapter practiceBring the chapter together: cross sections, the scattering amplitude, the integral equation and the Born approximation, Coulomb scattering, partial waves and phase shifts, the optical theorem, and scattering at low energy with its resonances. No worked example sits above the answers.Read lesson →

Mapping the lesson.

Scattering

Build the foundation