Physic Labs

Quantum mechanics

Quantum scattering

Watch a Gaussian wave packet reach a central Yukawa or Coulomb potential, scatter into outgoing wavefronts, and compare the angular distribution ∣f(θ)∣2|f(\theta)|^2 for screened V∝e−r/a/rV\propto e^{-r/a}/r versus unscreened potentials. Adjust the screening length a to see the distribution flatten.

Research

Equipment

  • Incoming wave packet and potential center on canvas
  • Slider switching Yukawa ↔ Coulomb potential
  • Screening-length slider a (0.4–3)
  • Time-step slider and angular-distribution plot $|f(\theta)|^2$

Procedure

  1. Follow the packet meeting the potential

    In figure 1, choose Yukawa mode and sweep the time slider: the packet advances from the left, crosses the center V(r), and splits into outgoing wavefronts plus a transmitted part — illustrating the first Born approximation for a weak potential.

  2. Compare Yukawa and Coulomb

    Switch the potential slider to Coulomb: the angular-distribution plot (figure 2) shows a dashed curve soaring at small angles because the 1/r1/r tail reaches far; screened Yukawa keeps the solid curve finite as θ→0\theta\to0 — σ(θ)\sigma(\theta) reflects the Fourier transform of the potential.

  3. Change the screening length and predict

    In Yukawa mode, drag a from 0.4 to 3.0: the depicted center grows and the ∣f(θ)∣2|f(\theta)|^2 curve sharpens at small angles since large a approaches the Coulomb limit. Predict the shape as a → 0 (nearly pointlike potential, almost isotropic scattering) then check.

Simulation

Experiment history

Scattering experiments shaped nuclear physics: in 1911 Ernest Rutherford inferred from the α-particle angular distribution measured by Geiger and Marsden that the atom's positive charge concentrates in a tiny nucleus — the Rutherford cross-section is exactly the Coulomb limit shown by the dashed curve. Max Born introduced the approximation bearing his name in 1926 while building quantum scattering theory and proposing the ∣ψ∣2|\psi|^2 probability interpretation. Hideki Yukawa used the e−r/a/re^{-r/a}/r form in 1935 for the nuclear force carried by a massive exchange particle — predicting the meson, found as the pion in 1947.

Related physicists

Max BornWerner HeisenbergHideki Yukawa

Related library topics

Quantum scattering