feat(QuantumMechanics/Blackbody): Added Canonical Definition Planck's law

[Sammybro11]

Description of Changes

New Directory at:
Physlib/QuantumMechanics/Blackbody to store further blackbody radiation related definitions and proofs.

New Files at:
Physlib/QuantumMechanics/Blackbody/PlancksLaw.lean Added definitions and positive and zero values lemmas for Spectral Radiance due to Planck's Law

Modified File at:
Physlib.lean added import for Planck's Law

Reviewer Guide

I have added frequency with Real number type right now but plan to make changes to that later when frequency is implemented. Also the conversion between frequency and wavelength can be added after that.

[github-actions]

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[nateabr]

Looks good! Some comments to fix

[nateabr]

spectralRadiance is not itself a physical constant, so putting it in Constants makes the API misleading. Could this be moved into a namespace such as Blackbody or another appropriate radiation namespace?

[Sammybro11]

Decided to name it Blackbody itself since the folder is also blackbody, other name possibly could have been EMR but that would intersect with EM based modules, so I just went with blackbody

[nateabr]

If we look at the definiton of spectralRadiance at T = 0, kB * (T : ℝ) = 0, therefore the computation below is 0/0, which in lean, by convention, is 0. Ofcourse mathematically, this proof is not valid even though the code has compiled.

We could define the physical formula only on positive frequency and temperature, and extend it by zero otherwise:

noncomputable def spectralRadiance (c : SpeedOfLight) (ν : ℝ) (T : Temperature) : ℝ := if 0 < ν ∧ 0 < (T : ℝ) then 2 * h * ν ^ 3 / ((c : ℝ) ^ 2 * (Real.exp (h * ν / (kB * (T : ℝ))) - 1)) else 0

Then the absolute-zero lemma reflects an explicit choice in the API, rather than Lean’s division convention. A later PR could state and prove that this extension agrees with the limit as $T \to 0^+$.

[Sammybro11]

That makes alot more sense, I was wondering why I was getting no errors. Thank you

[nateabr]

awaiting-author

[Sammybro11]

-awaiting-author

[nateabr]

Looks good to me, thanks

[jstoobysmith]

Looks good to me!