Exact energy eigenstates of the Coulomb-Stark Hamiltonian

An approximation-free, numerically efficient algorithm is presented for the Hamiltonian eigenstates of the Stark hydrogen problem describing a quantum particle exposed to the central Coulomb force and a homogeneous external field. As an example of application in a state expansion with continuous energy, we calculate the time dependent wave function of an electron tunneling from a hydrogen atom suddenly exposed to an external electric field.