Harmonic resonances and subquantization in the hydrogen emission spectrum

This work presents a new method for analyzing the hydrogen emission spectrum based on expressing orbital energies as exact rational fractions and identifying harmonic relationships between spectral lines. This approach reveals a resonance structure that remains hidden in classical units (nm, cm⁻¹) due to rounding and numerical limitations. The analysis demonstrates the existence of exact integer relationships, such as the 3:1 ratio between the H(5→4) and H(20→10) lines, as well as numerous other simple and complex harmonic resonances.

A fundamental unit of periodic photon energy — the subquantum unit [sQ] — is introduced. It corresponds to the energy of a single wave period in the state of super‑resonance. Using this unit, all examined lines of the Lyman, Balmer, Paschen, and Brackett series can be expressed as integer values forming a discrete resonance lattice with a modulus of ~18.64 GHz. This reveals a deeper harmonic organization of the atomic spectrum that has not been previously described.

The second part of the work introduces the Orbit Marker Algebra, in which the emission energy is expressed as the difference between two orbit markers — quantities characteristic of individual energy levels. These markers act as a “fingerprint” of the electron orbit and allow lossless calculations of transition energies with accuracy approaching the limit of 1/∞. The method enables reconstruction of the transition parameters based solely on the event marker.

In the third part, it is shown that transition energies can be written as ratios of integers, which makes it possible to identify harmonic resonances and relationships between spectral lines unambiguously. This approach enables systematic correction of spectroscopic data, including values published by NIST, by reducing the uncertainty factor.

The proposed Atomic Harmony Model reveals a deep mathematical symmetry of the hydrogen spectrum and leads to the concept of digital spectroscopy, in which the spectrum is described as a set of integers. These results may find applications in high‑resolution spectroscopy, astrophysics, the analysis of fundamental constants, and the precise calibration of cosmological data.