One hundred
years ago it was conjectured by Polya and Hilbert that the zeros of the Riemann
zeta function could be the eigenvalues of a quantum mechanical Hamiltonian. There are strong indications that this may be the case, however the so called Riemann Hamiltonian
has remained elusive so far. Building on previous works by Berry, Keating and Connes
we shall show that the Hamiltonian of an electron moving in a plane and subject to
the action of magnetic and electric fields could provide hints to this long standing
problem.