A Note on "The factor √(5/π) in d-, f- and g-type atomic orbitals and its possible relation to GEIER’s 6°=√(π/5) Rule - A structure-oriented analysis" by Stefan GEIER et al.
A Note on "The factor √(5/π) in d-, f- and g-type atomic orbitals and its possible relation to GEIER’s 6°=√(π/5) Rule - A structure-oriented analysis" by Stefan GEIER et al. This manuscript presents a remarkably clear and disciplined exploration of an idea that could easily have slipped into numerology, but does not. It starts from entirely orthodox quantum mechanics, works transparently with normalized spherical harmonics, and shows how √(5/π) arises in d‑, f‑ and g‑type orbitals for perfectly conventional reasons, while still using that appearance as a structural “bridge” to the independent GEIER √(π/5) programme. The care with which the authors separate what is derived from standard theory from what is conjectural is exemplary: they insist on a non‑tautological coefficient criterion, explicitly reject any claim of a “new constant of nature,” and consistently frame the GEIER link as a compatibility check rather than as proof. Equally impressive is the methodological attitud...
