Time-Independent Schrödinger Equation L1-312

Quantum MechanicsStationary quantum eigenproblemδ=5 · challengingL_DAG = 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

(- hba r^{2} /2 m \cdot L a pl a c ian + V (r)) p s i_{n} (r) = E_{n} p s i_{n} (r)

H*psi_n = E_n*psi_n with H = -(hbar^2/2m)*Laplacian + V(r); eigenstates form orthonormal basis; physical observables reduce to expectation values.

L-DAG

E.hamiltonian -> E.eigensolve -> O.spectra_wavefunctions

E.hamiltonianE.eigensolveO.spectra_wavefunctions

Well-posedness W

Existence:: true
Uniqueness:: true
Stability:: conditional
κ:: 500

Eigenvalues real under self-adjointness; inversion of V(r) from spectrum is the inverse Sturm-Liouville problem (ill-posed for incomplete data).

Solvability C

Solver class:: Iterative Lanczos / Davidson; finite-element basis; adjoint-eigenvalue for inversion
Convergence rate q:: 2
Complexity:: principle-dependent

Specs (0)

No L2 specs registered yet for this principle.