Time-Dependent Schrödinger Equation L1-313

Quantum MechanicsQuantum dynamicsδ=5 · challengingL_DAG = 3.5📋 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

i \cdot hba r \cdot d p s i / d t = (H_{0} + V_{l} a ser (t)) \cdot p s i (t)

i*hbar*dpsi/dt = H(t)*psi; includes laser-driven dynamics, wave-packet propagation.

L-DAG

E.hamiltonian_t -> E.laser_coupling -> D.time -> O.time_resolved

E.hamiltonian_tE.laser_couplingD.timeO.time_resolved

Well-posedness W

Existence:: true
Uniqueness:: true
Stability:: conditional
κ:: 700

Unitary evolution bounded; inversion ill-conditioned due to phase ambiguity.

Solvability C

Solver class:: Split-operator Fourier (SOFT); Crank-Nicolson; TDDFT if many-electron
Convergence rate q:: 2
Complexity:: principle-dependent

Specs (0)

No L2 specs registered yet for this principle.