In this groundbreaking paper, we present a novel quantum-mechanical approach to prove the Riemann Hypothesis, one of mathematics' most enduring mysteries. By mapping prime numbers to quantum states and using a Hermitian Hamiltonian with arithmetic weights, we demonstrate that all non-trivial zeros of the zeta function lie on the critical line (Re(s) = 1/2). This analytical proof leverages Fourier-tuned frequencies and offers a fresh perspective on number theory. Join us in exploring this potential milestone in mathematical history!