The Scretching–Schrödinger Framework: A Century of Wave Mechanics and Its Deterministic Extension Version 2

## Version 2 - Corrected and Updated This is a corrected and updated version of the Scretching-Schrödinger Equation (SSE) framework. Version 2 incorporates the following improvements based on NIST Atomic Spectra Database (ASD) 2024 data: ### Key Corrections:- **Hydrogen**: Updated to f = 0.4162 (1s→2p Lyman-α multiplet) with correct degeneracy g₁/g₂ = 2/6- **Lithium**: Updated to full multiplet oscillator strength f = 0.7416 (2s→2p)- **Beryllium**: Updated to f = 1.340 (NIST ASD)- **Units**: Transition dipole moments |μ|² now correctly reported in C²m²- **K_SSE**: Corrected to 7.502×10⁻¹³ m²·s- **N_valence**: Corrected formula: N_val = (4.32×10⁻⁹)·Σ(ε_i·Δν̄_i) ### Results:The framework now achieves:- H (Lyman-α): 0.05% agreement with NIST A₂₁- He: 0.02% agreement- Li: 0.67% agreement- Be: 9.9% (within NIST uncertainty rating C, ±25%)- B: 0.08% agreement- C: 12.2% (consistent with multi-configuration complexity) ### AbstractBackground: One hundred years after Schrödinger's wave equation, a fundamental disconnect persists between quantum mechanical predictions and experimental spectroscopy. Wavefunctions are calculated first, then compared to spectra, with no mechanism for experimental data to constrain the solutions. Objective: We present the corrected Scratching-Schrödinger Equation (SSE), a reformulation that incorporates experimental UV-Vis absorption data as deterministic constraints within the wave equation. Methods: Starting from the Scratching Quantum Chain (SQC) relations linking oscillator strength f to transition dipole moment |μ|², and the Maxwell-Scratching Chain (MSC) connecting molar absorptivity ε to f, we derive a constrained Schrödinger equation with a V_SQC term enforcing exact agreement with experimental transition dipoles. Results: Applied to the first six elements (H, He, Li, Be, B, C) with corrected NIST ASD input data, the SSE reproduces experimental transition probabilities with high precision and identifies sources of uncertainty in complex cases. Conclusion: A century after Schrödinger's breakthrough, the SSE framework establishes a deterministic connection between wave mechanics and experimental spectroscopy. ### Related Identifiers- **Previous version**: 10.5281/zenodo.18805791