feat(QuantumMechanics) : Prove potentialOperator_isSelfAdjoint

[ereinhardt8]

This pull request provides a proof for the lemma potentialOperator_isSelfAdjoint in Physlib/QuantumMechanics/RectangularBarrier/Basic.lean, which was previously an informal_lemma. Also, it proves potentialFunction_aestronglyMeasurable because potentialOperator_isSelfAdjoint uses it.

Specific Changes

Two informal lemmas were formalized and proved:

• RectangularBarrier.potentialFunction_aestronglyMeasurable : formalize and prove that the potential function of a rectangular barrier is almost everywhere strongly measurable
• RectangularBarrier.potentialOperator_isSelfAdjoint : prove that the potential function of a rectangular barrier is self adjoint using the above lemma

Reviewer Guide

I fixed any linting issues found in Physlib/QuantumMechanics/RectangularBarrier/Basic.lean after I ran lake exe lint_all and ./scripts/lint-style.sh locally.

The lemma potentialFunction_aestronglyMeasurable was only proved for the canonical volume measure. Is this an issue?

Additional Comments

I wrote the code, but used ChatGPT and Google Search to suggest approaches and next steps.

Thank you!

[github-actions]

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[jstoobysmith]

Hey @ereinhardt8 Many thanks for this first PR! Just one comment from me before this can be merged. It would be convention to not to have more then one tactic on a line e.g. swap; ext x; simp [...] should be three separate lines. Other then that, this PR looks great!

[jstoobysmith]

awaiting-author

[ereinhardt8]

Okay! I separated the lines that had multiple tactics.
-awaiting-author

[jstoobysmith]

Great! Many thanks! I've approved, and when the linters finish, I will merge this. So nothing else you need to do here.

Many thanks for this first PR! Hopefully the first of many.