Electronic Band Structure L1-316

Quantum MechanicsCrystal momentum eigenproblemδ=5 · challengingL_DAG = 3.2📋 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

(- hba r^{2} /2 m \cdot (g r a d + ik)^{2} + V_{c} r y s t (r)) u_{n, k} (r) = E_{n} (k) u_{n, k} (r)

Bloch theorem: psi_{n,k}(r) = e^{ik.r}*u_{n,k}(r); eigenvalues E_n(k) form bands; gap structure determines metal/insulator character.

L-DAG

E.crystal_potential -> E.eigensolve -> O.band_structure

E.crystal_potentialE.eigensolveO.band_structure

Well-posedness W

Existence:: true
Uniqueness:: true
Stability:: conditional
κ:: 600

Well-posed; DFT gap underestimate (Kohn-Sham gap problem); inverse structure→band mapping requires phase info.

Solvability C

Solver class:: DFT-LDA/GGA (VASP, Quantum ESPRESSO); tight-binding; GW (separate)
Convergence rate q:: 2
Complexity:: principle-dependent

Specs (0)

No L2 specs registered yet for this principle.