feat(QuantumMechanics): Fourier conjugate of the momentum operator#1433
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Add §C to Operators/Momentum.lean: the Fourier transform conjugates the momentum operator `𝐩 i = -iℏ∂ᵢ` into multiplication by the real symbol `2πℏ·ξᵢ` (`fourier_momentumCLM_eq`), via `𝐩 i` as `-iℏ` times the line derivative (`momentumCLM_eq_smul_lineDerivOp`). The symbol is packaged as `momentumSymbol i` with a `@[fun_prop]` temperate-growth lemma. Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
improve readability of `fourier_momentumCLM_eq`
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I've been mulling on this over the weekend and I'll be honest, I don't understand the ultimate purpose of this PR. def derivOperator (f : Space d → ℂ) : SpaceDHilbertSpace d →ₗ.[ℂ] SpaceDHilbertSpace d :=
unitaryConj (fourierUnitary d) (ℳ volume f)whose dense domain, adjoint, self-adjointness, etc. then follow from general properties of conjugation and |
Add §C to Operators/Momentum.lean: the Fourier transform conjugates the momentum operator
𝐩 i = -iℏ∂ᵢinto multiplication by the real symbol2πℏ·ξᵢ(fourier_momentumCLM_eq), via𝐩 ias-iℏtimes the line derivative (momentumCLM_eq_smul_lineDerivOp). The symbol is packaged asmomentumSymbol iwith a@[fun_prop]temperate-growth lemma.