What question did this study set out to answer?

This research aims to unify three foundational quantum phenomena through the brane-bulk framework.

May 22, 2026Open Access

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

Key Points

This research aims to unify three foundational quantum phenomena through the brane-bulk framework.
Analysis of electron orbital shapes using eigenvalue interference concepts.
Examination of Compton scattering as a mode transfer phenomenon between photons and electrons.
Investigation of the photoelectric effect based on threshold resonance and work function.
Demonstrated that electron orbital shapes correspond to standing wave patterns derived from spin waveforms.
Established that Compton scattering can be explained in terms of momentum transfer between radial and angular wave modes.
Clarified that the photoelectric effect requires photons to meet a specific energy threshold to release electrons.

Abstract

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 λC = ℏ/mₑ 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.

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

Key Points

Abstract

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