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 pseud...
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| Format: | Article |
| Language: | English |
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Wiley
2015-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2015/125832 |
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| author | Jeffrey M. Brown Miroslav Kolesik |
| author_facet | Jeffrey M. Brown Miroslav Kolesik |
| author_sort | Jeffrey M. Brown |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-d5fce4d78b2147c19f1db138e5e5a8a9 |
| institution | OA Journals |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-d5fce4d78b2147c19f1db138e5e5a8a92025-08-20T02:19:40ZengWileyAdvances in Mathematical Physics1687-91201687-91392015-01-01201510.1155/2015/125832125832Properties of Stark Resonant States in Exactly Solvable SystemsJeffrey M. Brown0Miroslav Kolesik1College of Optical Sciences, University of Arizona, Tucson, AZ 85721, USACollege of Optical Sciences, University of Arizona, Tucson, AZ 85721, USAProperties 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.http://dx.doi.org/10.1155/2015/125832 |
| spellingShingle | Jeffrey M. Brown Miroslav Kolesik Properties of Stark Resonant States in Exactly Solvable Systems Advances in Mathematical Physics |
| title | Properties of Stark Resonant States in Exactly Solvable Systems |
| title_full | Properties of Stark Resonant States in Exactly Solvable Systems |
| title_fullStr | Properties of Stark Resonant States in Exactly Solvable Systems |
| title_full_unstemmed | Properties of Stark Resonant States in Exactly Solvable Systems |
| title_short | Properties of Stark Resonant States in Exactly Solvable Systems |
| title_sort | properties of stark resonant states in exactly solvable systems |
| url | http://dx.doi.org/10.1155/2015/125832 |
| work_keys_str_mv | AT jeffreymbrown propertiesofstarkresonantstatesinexactlysolvablesystems AT miroslavkolesik propertiesofstarkresonantstatesinexactlysolvablesystems |