Schrödinger-Type Jacobi Operator

📘 „Description”: This work presents the construction and analysis of a self-adjoint Jacobi-type operator whose spectrum aligns with the imaginary parts of the nontrivial zeros of the Riemann zeta function. The operator is defined with a specific off-diagonal structure: f(n) = 1.034 · n^0.492 − [0.593 · sin(0.196·n + 0.107)] / [n^0.536 + 0.01 · log(n + 1)] Numerical computations confirm that the eigenvalues of the constructed operator match the first 100 scaled zeta zeros with high precision (mean squared error ≈ 3.8 × 10⁻²⁹). The operator also admits a differential form analogous to the Schrödinger operator with position-dependent mass. This result offers a concrete realization of the Hilbert–Pólya conjecture and supports the validity of the Riemann Hypothesis. All data, source code, and visualizations are included for full reproducibility. Author: Fabian BarańskiDate: May 18, 2025Language: English/PolishLicense: CC-BY 4.0 (recommended)