Hydrogen Atom

The τ-hydrogen atom is the simplest composite object in the τ-framework: a τ-proton (β-decay-differentiated τ-neutron) bound to a τ-electron via the electromagnetic sector at E₁. Its Bohr radius and Rydberg constant emerge as ι_τ-derived τ-categorical theorems, with SI numerical values recovered through the calibration cascade.

Categorical invariant. Two-defect-bundle composite (τ-proton + τ-electron) whose bound state on T² × R³ is governed by the τ-Schrödinger equation in the electromagnetic sector.

Primary registry anchor: IV.D496

Supporting items: IV.P126, IV.T238, IV.T28

1. I.K0 — Universe Postulate
2. IV.D02 — EM Sector at E₁
3. IV.T28 — τ-Schrödinger equation
4. IV.P126 — Bohr radius derived from ι_τ
5. IV.T238 — Bohr radius theorem
6. IV.D496 — Hydrogen atom as τ-categorical composite

Calibration anchor: PG-P01-neutron

Calibration chain:

1. m_n (anchor)
2. (m_n - m_p) via IV.T142
3. m_e via Yukawa hierarchy from ι_τ
4. ι_τ-derived α_em (fine-structure constant)
5. Bohr radius a₀ = ℏ / (m_e c α) recovered in SI

Manuscript reference: manuscript-sources/book-04/part06/ch45-hydrogen-atom-bohr-rydberg.tex

Status: Planned

Related glossary entries

• PG-P01-neutron τ-Neutron
• PG-Q01-mass Mass
• PG-L01-tau-schrodinger τ-Schrödinger Equation
• PG-C01-newton-g Newton's gravitational constant G

Referenced by

• PG-O02-alpha-particle α-Particle (Helium-4 Nucleus)
• PG-O05-helium-atom Helium Atom
• PG-O06-electron-orbital Electron Orbital