Quantum Well and Quantum Dot Electronic Structure L1-496

Semiconductor PhysicsConfined electronic statesδ=5 · challengingL_DAG = 3.6📋 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.

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Forward model E

H_{k . p} p h i_{n} = E_{n} p h i_{n} w i t h s t r ain - cor r ec t e d H ami l t o nian; (H_{k . p} + V_{H} + V_{x} c) p h i_{n} = E_{n} p h i_{n} (S C F)

Envelope-function k.p or tight-binding Hamiltonian for semiconductor nanostructures; Schrödinger-Poisson self-consistent for charged QDs; exchange-correlation via LDA/GGA.

L-DAG

E.strain -> E.kp_Hamiltonian -> O.iter -> O.states_transitions

E.strainE.kp_HamiltonianO.iterO.states_transitions

Well-posedness W

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

Well-posed; inversion for composition/strain from PL is ill-conditioned (multiple compositions produce same transition).

Solvability C

Solver class:: Finite element k.p + BiCGSTAB; self-consistent SCF with Broyden mixing; inversion by Bayesian MCMC
Convergence rate q:: 2
Complexity:: O(N_states * N_grid^2)

Specs (0)

No L2 specs registered yet for this principle.