Harmonic resonances and subquantization in the hydrogen emission spectrum

Abstract

An alternative method for analyzing the hydrogen spectrum is presented, based on recording orbital energies as precise fractions, which allows the identification of harmonic relationships between lines not visible in standard rounded data. Among other things, an exact 3:1 relationship between the H(5→4) and H(20→10) lines is demonstrated. The fundamental unit of photon energy ε₀ and the corresponding subquantum unit [sQ] were introduced. All analyzed lines of the Lyman , Balmer , Paschen , and Brackett series (n ≤ 7, m ≤ 4) form a discrete resonant lattice with a modulus of ~18.64 GHz , suggesting the existence of a deeper harmonic organization of the spectrum. The method provides an analytical tool allowing for more precise organization of spectroscopic data and may find applications in high-resolution spectroscopy, astrophysics, and the analysis of fundamental physical constants.