Electron Orbital

A τ-electron orbital is a single-particle eigenmode of the τ-Schrödinger operator in an EM-sector central potential — the τ-categorical projection of the Bohr-style structure that organizes the periodic table. The (n, ℓ, m) labels arise as winding numbers on T² × R³ and the orbital occupancy follows the Dual Magic Number Structure (IV.T254).

Categorical invariant. Single-particle eigenmode of the τ-Schrödinger operator in an EM-sector central potential, indexed by T² winding numbers (n, ℓ, m).

Primary registry anchor: IV.T296

Supporting items: IV.D02, IV.T28, IV.T254

1. I.K0 — Universe Postulate
2. IV.D02 — EM Sector at E₁
3. IV.T28 — τ-Schrödinger equation
4. IV.P126 — Bohr radius from ι_τ — sets the orbital length scale
5. IV.T296 — Hydrogen Ground State theorem (1s orbital)
6. IV.T254 — Dual Magic Number Structure (T²-shell occupancy)

Numerical value: 5.29177210903e-11 ± 8.0e-21 m

Calibration anchor: PG-P01-neutron

Calibration chain:

1. m_n (anchor)
2. m_e via Yukawa hierarchy from ι_τ
3. ι_τ-derived α_em (fine-structure)
4. Bohr radius a₀ = ℏ / (m_e c α) sets the orbital length scale
5. (n, ℓ, m) labels from T² winding numbers

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

Status: Planned

Related glossary entries

• PG-P01-neutron τ-Neutron
• PG-O01-hydrogen-atom Hydrogen Atom
• PG-O05-helium-atom Helium Atom
• PG-Q01-mass Mass
• PG-L01-tau-schrodinger τ-Schrödinger Equation