A Quantum Hamiltonian Framework for the Riemann Hypothesis: Spectral Analysis and Eigenvalue Alignment

Presented is a framework of the Riemann Hypothesis (RH) by constructing a self-adjoint Hamiltonian operator whose eigenvalues correspond to the nontrivial zeros of the Riemann zeta function. Using spectral analysis, functional analysis, and quantum mechanical methods, we show that the spectral properties of the constructed Hamiltonian compel all eigenvalues to reside on the critical line as a direct consequence of its self-adjointness and boundary conditions. Furthermore, we employ numerical verification, spectral uniqueness, and eigenvalue quantization conditions to support the framework. Computational analyses and numerical simulations further strengthen the argument, establishing a bridge between quantum mechanics and number theory within a time-free physics framework.