Quantum Scattering Theory L1-314

Quantum MechanicsS-matrix and phase shiftsδ=5 · challengingL_DAG = 3.3📋 Stub — not mineable

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Unclaimed Principle — open for contribution

This Principle is declared in the catalog but has no reference solver, no pinned dataset, and is not registered on-chain. There is no reward pool. Submitting a cert against this Principle today will record the cert for reproducibility but pay zero PWM.

To claim it as a Bounty #7 contribution: open a PR adding (1) a reference solver, (2) ≥1 dataset pinned to IPFS, (3) updates to the L3 manifest with dataset CIDs. After verifier-agent triple-review, the founders' 3-of-5 multisig signs PWMRegistry.register() and the Principle becomes mineable.

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Forward model E

p s i_{k} (r) e^{(} ik . r) + f (t h e t a) \cdot e^{(} ik r) / r; f (t h e t a) = l \sum (2 l + 1) \cdot e^{(} i \cdot d e l t a_{l}) \cdot s in (d e l t a_{l}) \cdot P_{l} (cos t h e t a) / k

Lippmann-Schwinger: psi = psi_0 + G_0 * V * psi; scattering amplitude f(k',k); phase shifts delta_l from partial-wave analysis.

L-DAG

E.lippmann_schwinger -> E.eigensolve -> O.cross_section

E.lippmann_schwingerE.eigensolveO.cross_section

Well-posedness W

Existence:: true
Uniqueness:: true
Stability:: conditional
κ:: 400

Well-posed forward; inverse scattering (reconstructing V from f(E,theta)) is Borg-Marchenko-style; unique with phase info.

Solvability C

Solver class:: Numerov integration per partial wave; Kohn variational method
Convergence rate q:: 2
Complexity:: principle-dependent

Specs (0)

No L2 specs registered yet for this principle.