  We construct a formally self-adjoint Hamiltonian whose eigenvalues correspond
to the nontrivial zeros of the Riemann zeta function. We consider a
two-dimensional Hamiltonian which couples the Berry-Keating Hamiltonian to the
number operator on the half-line via a unitary transformation. We demonstrate
that the unitary operator, which is composed of squeeze (dilation) operators
and an exponential of the number operator, confines the eigenfunction of the
Hamiltonian to one dimension as the squeezing parameter tends towards infinity.
The Riemann zeta function appears at the boundary of the resulting confined
wave function and vanishes as a result of the imposed boundary condition. If
the formal argument presented here can be made more rigorous, particularly if
it can be shown rigorously that the Hamiltonian remains self-adjoint under the
imposed boundary condition, then our approach has the potential to imply that
the Riemann hypothesis is true.
