rationalskepticism.org

A Hamiltonian operator Hˆ is constructed with the property that if the eigenfunctions obey a suitable boundary condition, then the associated eigenvalues correspond to the nontrivial zeros of the Riemann zeta function. The classical limit of Hˆ is 2xp, which is consistent with the Berry- Keating conjecture. While Hˆ is not Hermitian in the conventional sense, iHˆ is PT symmetric with a broken PT symmetry, thus allowing for the possibility that all eigenvalues of Hˆ are real. A heuristic analysis is presented for the construction of the metric operator to define an inner-product space, on which the Hamiltonian is Hermitian. If the analysis presented here can be made rigorous to show that Hˆ is manifestly self-adjoint, then this implies that the Riemann hypothesis holds true.