SQC Extensions to Hydrogen Fine-Structure Phenomena: Lamb Shift, Hyperfine Structure, Zeeman Effect, Stark Effect, and the B12 = B21 Einstein Coefficient Invariants

This paper extends the Scretching Quantum Chain (SQC) far beyond its previously developed applications to the Lamb shift, hyperfine structure, and Zeeman effect by introducing two new invariant-based branches of the framework. First, it develops an SQC treatment of the Stark effect, covering both linear and quadratic regimes, and derives new SQC–Stark invariants, a parameter-free electric-field sensitivity coefficient, and a complete Stark multiplet sum rule. Second, it expands the SQC into the Einstein B-coefficient domain, showing that the absorption and stimulated-emission coefficients, B12 and B21, together generate two new dimensionless invariants, Ψ1 and Ψ2. Among these, Ψ2 is especially significant because it yields a direct experimental determination of oscillator strength f12 from B12 alone, presented here as a new result not found in standard quantum-optics treatments. The paper also introduces a symmetric invariant, Xsym, that captures the degeneracy structure of both lower and upper states simultaneously, thereby extending the algebraic reach of the SQC formalism while preserving exact reduction to the standard SQC law in the zero-perturbation limit. Using six hydrogen transitions from the Lyman and Balmer series, the study provides numerical verification against NIST data together with full graphical validation. Overall, the work positions the SQC as a broader deterministic radiative framework capable of unifying spontaneous emission, stimulated processes, and field-induced spectral perturbations under one constant-sloped invariant structure.