Wavefunction-to-Stationary Oscillation Bridge in USP Field Theory: An Operational Mapping for the Electron

This work presents an operational bridge between the standard quantum-mechanical wavefunction and the USP Field Theory interpretation of a bound electron as a stationary resonance corridor mode. The document does not replace the Schrodinger equation, the Born rule, standard atomic spectroscopy, quantum electrodynamics, detector theory, spinor algebra, or established hydrogenic energy levels. Instead, it provides a geometry-first interpretation layer in which the spatial wavefunction envelope maps to a positive stationary-corridor energy density through the relation u(r) = kappa |psi(r)|^2, with the normalization constant kappa fixed by a declared bound-state energy anchor. Version v1.1.1 strengthens the original public v1.0 release by clarifying the state-dependent meaning of kappa, adding a Coulomb-detuning proxy with validity-range guardrails, separating the energy-derived detuning proxy Delta f_C from the geometric corridor-frequency scale f_corr = c/(2 pi r), and refining detector coupling as spatial, temporal, and resonance-gated uptake from an extended stationary mode. The document also includes worked hydrogenic 1s and 2p_z examples, detector-kernel falsification protocols, bandwidth/gating tests, statistical decision rules, confound controls, and a reproducibility appendix. This version also adds an interpretive note on spin as boundary-closure shorthand. The standard spin label is preserved exactly as in quantum mechanics, while USP interprets spin-1/2 as a compact marker of a deeper boundary-closure topology whose spinor phase structure closes after 4 pi rather than an ordinary 2 pi scalar cycle. In the atomic regime this full topology does not need to be dynamically resolved; the standard spin quantum number remains sufficient for exclusion rules, magnetic coupling, and state counting. Non-replacement statement: USP Field Theory does not replace quantum mechanics, the Schrodinger equation, the Born rule, the Dirac equation, spinor algebra, Pauli exclusion, QED, standard spectroscopy, or detector theory. It provides an interpretive and operational geometry layer for understanding stationary electron states, orbital structure, and localized measurement events.

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-06-28
DOI
https://doi.org/10.5281/zenodo.20991300
Primary Topic
Quantum Mechanics and Applications
Type
preprint
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preprint

Wavefunction-to-Stationary Oscillation Bridge in USP Field Theory: An Operational Mapping for the Electron

Sadegh Sepehri
Zenodo (CERN European Organization for Nuclear Research)
Quantum Mechanics and Applications
preprint

Wavefunction-to-Stationary Oscillation Bridge in USP Field Theory: An Operational Mapping for the Electron

Sadegh Sepehri
preprint en

Abstract

This work presents an operational bridge between the standard quantum-mechanical wavefunction and the USP Field Theory interpretation of a bound electron as a stationary resonance corridor mode. The document does not replace the Schrodinger equation, the Born rule, standard atomic spectroscopy, quantum electrodynamics, detector theory, spinor algebra, or established hydrogenic energy levels. Instead, it provides a geometry-first interpretation layer in which the spatial wavefunction envelope maps to a positive stationary-corridor energy density through the relation u(r) = kappa |psi(r)|^2, with the normalization constant kappa fixed by a declared bound-state energy anchor. Version v1.1.1 strengthens the original public v1.0 release by clarifying the state-dependent meaning of kappa, adding a Coulomb-detuning proxy with validity-range guardrails, separating the energy-derived detuning proxy Delta f_C from the geometric corridor-frequency scale f_corr = c/(2 pi r), and refining detector coupling as spatial, temporal, and resonance-gated uptake from an extended stationary mode. The document also includes worked hydrogenic 1s and 2p_z examples, detector-kernel falsification protocols, bandwidth/gating tests, statistical decision rules, confound controls, and a reproducibility appendix. This version also adds an interpretive note on spin as boundary-closure shorthand. The standard spin label is preserved exactly as in quantum mechanics, while USP interprets spin-1/2 as a compact marker of a deeper boundary-closure topology whose spinor phase structure closes after 4 pi rather than an ordinary 2 pi scalar cycle. In the atomic regime this full topology does not need to be dynamically resolved; the standard spin quantum number remains sufficient for exclusion rules, magnetic coupling, and state counting. Non-replacement statement: USP Field Theory does not replace quantum mechanics, the Schrodinger equation, the Born rule, the Dirac equation, spinor algebra, Pauli exclusion, QED, standard spectroscopy, or detector theory. It provides an interpretive and operational geometry layer for understanding stationary electron states, orbital structure, and localized measurement events.

Zenodo (CERN European Organization for Nuclear Research)
Peace, Justice and strong institutions
Quantum Mechanics and Applications
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