Perturbation theory of resonant states induced by an electrostatic field: one-dimensional model

The behaviour of an electron in an attractive potential placed in a uniform external electrostatic field is studied in a one-dimensional model. The time development of the state is obtained through the evolution operator, which can be expressed in terms of resonant outgoing-wave energy eigenfunctions with complex energies. The theory, perturbative and non-perturbative is developed with the aid of Kapur-Peierls eigenfunctions and Bloch's boundary-condition operator.