Paper XXXI of the Brane-Bulk Series Orbital Shapes, Compton Scattering, and the Photoelectric Eect B. D. Jagadeesan, MD

Three foundational phenomena of quantum mechanics are unied under two complementary concepts derived from the brane-bulk framework. (1) Electron orbital shapes arise from eigenvalue interference: the self-interference of the spin waveform as the electron wraps around a nucleus, generating the characteristic nodal patterns of s, p, d, f orbitals as standing waves of the angular harmonic modes (Paper VIII). (2) Compton scattering is mode transfer: a photon (radial wave mode, Paper VI) collides with an electron (angular wave mode, Paper VIII), transferring momentum between modes. The Compton wavelength λ_C = ℏ/m_e c is the spatial period of the electron spin-1/2 oscillation the length over which one full spin cycle occurs. (3) The photoelectric eect is threshold resonance: a photon must have energy E = hν ≥ϕ (work function) to excite the electron from its standing wave eigenstate into a free propagating mode. Part of the One-Octonion Brane-Bulk Framework series. Anchor DOI: 10.5281/zenodo.19120873. Community: one-octonion-brane-bulk. Author: Bharathi Dasan Jagadeesan, M.D., University of Minnesota. ORCID: 0000-0002-1143-941X.