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feat(QuantumMechanics): Fourier conjugate of the momentum operator#1433

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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.

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Thank you for this PR, which will now be reviewed. If submitting to ./Physlib or ./QuantumInfo, please see our review guidelines if you are not familiar with the process. You should expect a back and forth with a reviewer before your PR is merged. See also that link for how to add appropriate labels to your PR. The PR will also go through a number of automated checks. You can learn more about these here, including how to run them locally.

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@github-actions github-actions Bot added the t-quantum-mechanics Quantum mechanics label Jul 17, 2026
@gloges gloges self-assigned this Jul 18, 2026
adambornemann-glitch and others added 2 commits July 19, 2026 13:38
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`
@adambornemann-glitch
adambornemann-glitch force-pushed the feat/momentum-fourier-identity branch from 05ef667 to 53e72b4 Compare July 19, 2026 17:57
@gloges

gloges commented Jul 19, 2026

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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.
You've been building all of the machinery to get a great definition for any derivative operator,

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 mulOperator. Limiting ourselves to only momentum (linear f) in a funny way makes things both less generally applicable and harder to prove (unimportant details of f get in the way). Let's discuss and come up with a plan of attack on the Zulip.

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