Quantum Proof of Riemann Hypothesis

Enlightened by the G-dynamics being identified as a part of quantum covariant Hamiltonian system (\textbf{QCHS}) for constructing the geometric wave equation based on the quantum covariant Poisson bracket (\textbf{QCPB}) theory, we find a new quantum physical system associated with classical Hamiltonian operator ${\hat{H}}^{\left( cl \right)} $ in Schr\"{o}dinger equation $\sqrt{-1}\hbar \frac{\partial}{\partial t} \varphi ={\hat{H}}^{\left( cl \right)} \varphi$ behind the Riemann non-trivial zeroes, such an unbounded linear self-adjoint operator ${{\hat{w}}^{\left( cl \right)}}={{b}_{c}}\hat{Q} $ to solve the Hilbert-P\'{o}lya conjecture (\textbf{HPC}) really exists that is given by one of geometric wave equation, that's exactly what Hilbert-P\'{o}lya and Berry-Keating still expect to find such peculiar quantum system in proving the Riemann hypothesis over the long time, and with identity ${{\hat{w}}^{\left( cl \right)}}{{u}^{-1/2}}=\hat{Q}{{u}^{-1/2}}=0$ holds, then Riemann hypothesis (\textbf{RH}) is then proven. Meanwhile, we discuss the curvature operator $\hat{Q}$ in different dimensional case, especially, Laplacian-Bertrami operator is considered for curvature operator. The relation between the Schr\"{o}dinger equation and geometric wave equation associated with geometric Hamiltonian operator is given.For the Berry-Keating conjecture (\textbf{BKC}), we need to find this unknown physical system, so that we comprehensively consider the Riemann manifold, Einstein metric and Ricci flow to ensure what the imaginary part really stands for, then it connects the vacuum field equation in two dimensional case, the scalar curvature forms a discrete set in 2D Riemann manifolds.