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Main Author:	Scretching, Daniel
Format:	Recurso digital
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Published:	Zenodo 2026
Online Access:	https://doi.org/10.5281/zenodo.19078872
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<div> <div> <div> <div> <div dir="auto"> <div> <div> Description The SQC Invariant in Hydrogenic Theory III: The Exact Connection Between the Two SQC Scretching Invariants completes a three-part investigation into the structure of radiative invariants in hydrogenic systems by establishing a precise algebraic equivalence between two previously derived SQC quantities. Building directly on earlier results, this work demonstrates that the spontaneous-emission time constant and the stimulated-radiation cofactor are not independent constructs but rather complementary expressions of the same underlying electromagnetic content. The first invariant, associated with spontaneous emission, governs the Einstein A-coefficient sector and encodes the characteristic radiative decay timescale. The second invariant, tied to stimulated processes, governs the Einstein BBB-coefficient sector and captures the coupling strength to external radiation fields. Using the standard Einstein relations in the ordinary-frequency convention, the paper derives an exact proportionality linking these two quantities through a simple conversion factor involving fundamental constants. This result shows that JSQC=c38πh ISQC, ISQC=8πhc3 JSQC,J_{\text{SQC}} = \frac{c^3}{8\pi h} \, I_{\text{SQC}}, \quad I_{\text{SQC}} = \frac{8\pi h}{c^3} \, J_{\text{SQC}},JSQC=8πhc3ISQC,ISQC=c38πhJSQC, establishing that the two invariants are algebraically interchangeable representations connected by the spontaneous-to-stimulated transition framework originally formulated by Albert Einstein. In this interpretation, the distinction between spontaneous and stimulated emission is not a separation of constants, but a redistribution of the same invariant structure across different radiative regimes. The analysis carefully adheres to standard conventions, including the ordinary-frequency formulation of Einstein coefficients and established degeneracy relations. Consistency with modern physical constants is maintained through the use of National Institute of Standards and Technology CODATA 2022 values, and the treatment aligns with established literature such as the review by Robert C. Hilborn. Overall, this paper clarifies that the SQC invariants do not introduce new physics, but instead reveal a hidden algebraic unity within the standard radiative formalism. By explicitly connecting the AAA- and BBB-coefficient sectors, it provides a compact and conceptually transparent framework for understanding how spontaneous and stimulated processes arise from the same fundamental electromagnetic structure. </div> </div> </div> </div> <div> </div> </div> </div> </div> <div> </div>

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