Properties of Stark Resonant States in Exactly Solvable Systems

Properties of Stark resonant states are studied in two exactly solvable systems. These resonances are shown to form a biorthogonal system with respect to a pairing defined by a contour integral that selects states with outgoing wave boundary conditions. Analytic expressions are derived for the pseudonorm, dipole moment, and coupling matrix elements which relate systems with different strengths of the external field. All results are based on explicit calculations made possible by a newly designed integration method for combinations of Airy functions representing resonant eigenstates. Generalizations for one-dimensional systems with short-range potentials are presented, and relations are identified which are likely to hold in systems with three spatial dimensions.