The hydrogen atom — where quantum mechanics was born. In LFM, atomic spectra emerge from electron standing waves in the proton's χ field.
Balmer (1885): Found empirical formula for visible hydrogen lines. Bohr (1913): Explained it with quantized electron orbits.
E_n = −13.6 eV / n²
In LFM, the proton creates a tiny χ depression. The electron wavefunction (ψ) satisfies the spinor wave equation (GOV-01-S) in this potential. Standing wave solutions require quantized angular momentum, yielding discrete energy levels.
Note: At atomic scales, χ/χ₀ ≈ 1 − 10⁻⁴⁴ — the correction is immeasurably small. LFM reproduces standard QM predictions exactly at these scales.
Click on Balmer lines above to see transitions. Energy levels scale as -13.6/n² eV.
| Transition | Wavelength | Energy | Region |
|---|---|---|---|
| Hα | 656.11 nm | 1.890 eV | Visible |
| Hβ | 486.01 nm | 2.551 eV | Visible |
| Hγ | 433.94 nm | 2.857 eV | Visible |
| Hδ | 410.07 nm | 3.023 eV | Visible |
| Hε | 396.91 nm | 3.124 eV | Visible |
| n=8 → n=2 | 388.81 nm | 3.189 eV | Visible |
Hydrogen spectrum discovered by Balmer (1885), explained by Bohr (1913), formalized by Schrödinger (1926).
LFM reproduces standard predictions (χ ≈ χ₀ at atomic scales).