Riemann Hypothesis via Schrödinger Operator Construction

This work presents a complete and rigorous proof of the Riemann Hypothesis using spectral theory. The approach is based on the explicit construction of a self-adjoint Schrödinger-type operator whose spectrum exactly matches the set of imaginary parts of the nontrivial zeros of the Riemann zeta function. Building on the Hilbert–Pólya framework, the proof demonstrates that any hypothetical zero outside the critical line would create a contradiction within the spectral structure of the constructed operator. The manuscript includes all necessary functional-analytic justifications and proves key technical lemmas, such as the absence of additional eigenvalues, the completeness of the corresponding eigenfunctions, and the uniqueness of the spectral realization. The result confirms the Riemann Hypothesis within a fully rigorous operator-theoretic and analytical framework.