The Scretching–Schrödinger Framework: A Century of Wave Mechanics and Its Deterministic Extension (Version.1)

Description

In 1926, Erwin Schrödinger introduced the wave equation that transformed physics and chemistry, providing the mathematical foundation for atomic structure, molecular bonding, and modern quantum theory. For a century, the Schrödinger equation has enabled the calculation of wavefunctions and energy levels. Yet its practical workflow has remained fundamentally one-directional: solve the equation first, then compare predicted transitions to experimental spectra.

The Scretching–Schrödinger Framework proposes a structural extension of wave mechanics that eliminates this separation.

At its core is the Scretching–Schrödinger Equation (SSE) — a constrained reformulation of Schrödinger’s equation that embeds experimentally measured UV-Vis absorption data directly into the quantum operator through a deterministic correction term. Instead of spectroscopy merely validating theory after the fact, experimental oscillator strengths and transition dipole moments become internal constraints that shape admissible solutions of the wave equation itself.

This framework builds upon two previously developed chains:

• Scretching Quantum Chain (SQC): linking oscillator strength fff to transition dipole moment ∣μ∣2|\mu|^2∣μ∣2.

• Maxwell–Scretching Chain (MSC): connecting molar absorptivity ε\varepsilonε to oscillator strength and electromagnetic observables.

By synthesizing these relations, the SSE introduces a new potential term VSQCV_{\text{SQC}}VSQC that enforces exact agreement between calculated and measured transition dipoles. The result is a bidirectional bridge between quantum wave mechanics and measurable spectroscopy.

Scope and Validation

Version 1 applies the SSE framework across the entire periodic table—from hydrogen (Z = 1) to oganesson (Z = 118). Using NIST-referenced spectroscopic data as deterministic constraints, the framework reports:

• Identity-level regressions (R² = 1.000)

• Relative errors below 0.001%

• Exact recovery of transition energies and oscillator strengths

• Reverse derivation of quantum defects and radial integrals

• Extraction of valence electron counts and shell closure indicators from single UV-Vis measurements

Nineteen derived equations formalize these inversion procedures, allowing measurable absorption data to reconstruct internal quantum structure.

Conceptual Contribution

The historical arc from Schrödinger’s formulation in Arosa to modern spectroscopy has treated experiment and wave mechanics as sequential stages. The Scretching–Schrödinger Framework proposes a structural unification:

• Wavefunctions are no longer free solutions awaiting comparison.

• Experimental dipole strengths become governing constraints.

• Spectroscopy becomes an intrinsic operator-level element of quantum mechanics.

This marks a shift from predictive-only wave mechanics toward a deterministic, measurement-integrated formalism.

Position Within Quantum Theory

The framework does not alter the foundational structure of quantum mechanics. Instead, it introduces a constraint-based extension that embeds empirical electromagnetic observables directly within the Schrödinger operator. The result is a closed algebraic chain linking:

Quantum Electrodynamics → Oscillator Strength → UV-Vis Absorbance → Wavefunction Constraint → Atomic Structure

By internalizing experimental reality into the equation itself, the Scretching–Schrödinger Equation presents a deterministic extension of wave mechanics at the centennial milestone of Schrödinger’s breakthrough.