Randomized trial shows match of harmonic energy levels with spectral lines, highlighting fundamental quantum relationships.
PHM energy levels E_p = p^2 * Ry, fitted with a single scale factor, match 84% of atomic spectral transitions across H, He, Li, C, N, O, Na, Fe, Xe from the NIST Atomic Spectra Database. He, C, Na, Xe achieve 100% match within 10%. The value Eₚ₌₁ = 13.6 eV equals the hydrogen ionization energy exactly.
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Will Daoud (2026) studied this question.
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