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feat(QuantumMechanics/Blackbody): Formalize Wien's displacement law - #1721

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@dwan-ith dwan-ith commented Oct 2, 2026

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  • Wien's Displacement Law:
    • Auxiliary function $h_n(x) = x - n(1 - e^{-x})$ and its derivative
    • Existence and uniqueness of positive root via IVT and strict monotonicity
    • Physical constants $x_5$ (wienConstant5) and $x_3$ (wienConstant3)
    • Rigorous enclosures $4 < x_5 < 5$ and $2 < x_3 < 3$ (0 sorry)
    • Global maxima of physical radiance curves (isMaxOn)
    • Wien's displacement laws: $\lambda_1 T_1 = \lambda_2 T_2$ and $\nu_1/T_1 = \nu_2/T_2$
    • Proof that wavelength and frequency peaks differ (wien_roots_differ)

…isplacement law

Formalizes the project idea 'Planck's Theory of Blackbody Radiation' from https://physlib.io/project-ideas.

Key additions:
- Frequency and wavelength forms of Planck's spectral radiance
- Positivity, absolute-zero limits, correspondence between forms
- First and second radiation constants
- Wien auxiliary function h(x) = x - n(1 - e^{-x})
- Existence and uniqueness of the positive Wien root (IVT + monotonicity)
- Named Wien constants x5 ≈ 4.9651 (wavelength) and x3 ≈ 2.8214 (frequency)
- Rigorous enclosures 4 < x5 < 5 and 2 < x3 < 3 (no sorry)
- Global maxima of spectral radiance curves (isMaxOn)
- Wien's displacement laws: λ₁T₁ = λ₂T₂ and ν₁/T₁ = ν₂/T₂
- Proof that wavelength and frequency peaks differ (wien_roots_differ)
@github-actions github-actions Bot added the large label Oct 2, 2026
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github-actions Bot commented Oct 2, 2026

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@github-actions github-actions Bot added the t-quantum-mechanics Quantum mechanics label Oct 2, 2026
@jstoobysmith jstoobysmith added the blocked-by-PR This PR depends on another PR label Oct 2, 2026

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