### Abstract

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.

Original language | English (US) |
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Article number | 125832 |

Journal | Advances in Mathematical Physics |

Volume | 2015 |

DOIs | |

State | Published - 2015 |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)
- Applied Mathematics

### Cite this

*Advances in Mathematical Physics*,

*2015*, [125832]. https://doi.org/10.1155/2015/125832

**Properties of Stark Resonant States in Exactly Solvable Systems.** / Brown, Jeffrey M.; Kolesik, Miroslav.

Research output: Contribution to journal › Article

*Advances in Mathematical Physics*, vol. 2015, 125832. https://doi.org/10.1155/2015/125832

}

TY - JOUR

T1 - Properties of Stark Resonant States in Exactly Solvable Systems

AU - Brown, Jeffrey M.

AU - Kolesik, Miroslav

PY - 2015

Y1 - 2015

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84957064193&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84957064193&partnerID=8YFLogxK

U2 - 10.1155/2015/125832

DO - 10.1155/2015/125832

M3 - Article

AN - SCOPUS:84957064193

VL - 2015

JO - Advances in Mathematical Physics

JF - Advances in Mathematical Physics

SN - 1687-9120

M1 - 125832

ER -