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jstoobysmith
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Added one comment here, but there are also a couple of comments on the Lean Zulip, which should be discussed.
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| @[inherit_doc QuantumMechanics.angularMomentum3DOperator] | ||
| scoped[AngularMomentum] notation "𝓛x" => QuantumMechanics.angularMomentum3DOperator 0 |
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I wouldn't define this, maybe we just come up with a notation for a general QuantumMechanics.angularMomentum3DOperator i?
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awaiting-author |
Use indexed notation and DimThree names for the new component API. Generalize crossProductVee to arbitrary coefficients and reuse it with the transpose that preserves the angular-momentum sign convention. AI assistance: Codex (GPT-6 Astra). Co-authored-by: GPT-6 Astra <noreply@openai.com>
This extends the angular-momentum operators from #1673 on the common invariant Schwartz domain. It transports the existing Schwartz-space
𝐋²to a densely defined Hilbert-space operator, proves its component-sum formula and symmetry, and identifies the right-handed 3D componentsLx = L₁₂,Ly = L₂₀,Lz = L₀₁. The Schwartz and Hilbert-space APIs then establish the Levi-Civita/cyclic commutation relations and the identities[Lz,L±] = ±ℏ L±and[L²,L±] = 0. Hilbert-space commutators are stated pointwise on Schwartz vectors with membership proofs for intermediate applications. No new dependency is added.Reviewer map: Start with the
angularMomentumSqOperatoradditions inAngularMomentum.lean, then readThreeDimensional.leanin order: Cartesian components, commutation algebra, ladder operators.API-map.yamlandPhyslib.leanrecord the API and new import.Local validation: On the latest
upstream/master, Lake rebuilt both changed angular-momentum modules and their hydrogen downstream module. Focused Lean linters (15 checks on both modules), axiom audit, import check, API-map check, style check, codespell, andgit diff --checkpassed. On this Windows machine,lake --no-cache exe lint_allcannot start its native C dependencies becauseccis unavailable.AI assistance: Codex (GPT-6 Astra).