  Towards the Hilbert-P\'olya conjecture, in this paper, we present a general
construction of Hamiltonian $\hat{H}_{f},$ which leads a general family of
Hurwitz zeta functions $(-1)^{z_{n}-1}L(f,z_{n},x+1)$ defined by Mellin
transform becomes their eigenstates under a suitable boundary condition, and
the eigenvalues $E_{n}$ have the property that $z_{n}=\frac{1}{2}(1-iE_{n})$
are the zeros of a general family of zeta functions $L(f,z)\equiv L(f,z,1)$.
