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Advances in Mathematical Physics
Volume 2015, Article ID 125832, 11 pages
Research Article

Properties of Stark Resonant States in Exactly Solvable Systems

College of Optical Sciences, University of Arizona, Tucson, AZ 85721, USA

Received 15 September 2015; Revised 23 November 2015; Accepted 29 November 2015

Academic Editor: Emmanuel Lorin

Copyright © 2015 Jeffrey M. Brown and Miroslav Kolesik. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.