Hierarchy of sum rules for oscillator strengths
It is shown that the well known sum rules for oscillator strengths for Hydrogen atom can be generalised to a whole class of sum rules. The sum rules have contributions from the discrete and the continuum parts of the spectrum neither of which can be calculated in closed analytical form but can be ca...
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| Format: | Working paper |
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2018
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| _version_ | 1826259371071373312 |
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| author | Sukumar, C |
| author_facet | Sukumar, C |
| author_sort | Sukumar, C |
| collection | OXFORD |
| description | It is shown that the well known sum rules for oscillator strengths for Hydrogen atom can be generalised to a whole class of sum rules. The sum rules have contributions from the discrete and the continuum parts of the spectrum neither of which can be calculated in closed analytical form but can be calculated numerically. The numerical calculations are carried out to check the validity of the sum rules. The procedure for constructing sum rules for general potentials is discussed. Generalisations of Kramers relations and the Virial theorem are discussed. |
| first_indexed | 2024-03-06T18:48:47Z |
| format | Working paper |
| id | oxford-uuid:0f766053-103c-4c95-a102-14eae4f27f4b |
| institution | University of Oxford |
| last_indexed | 2024-03-06T18:48:47Z |
| publishDate | 2018 |
| record_format | dspace |
| spelling | oxford-uuid:0f766053-103c-4c95-a102-14eae4f27f4b2022-03-26T09:51:21ZHierarchy of sum rules for oscillator strengthsWorking paperhttp://purl.org/coar/resource_type/c_8042uuid:0f766053-103c-4c95-a102-14eae4f27f4bSymplectic Elements at Oxford2018Sukumar, CIt is shown that the well known sum rules for oscillator strengths for Hydrogen atom can be generalised to a whole class of sum rules. The sum rules have contributions from the discrete and the continuum parts of the spectrum neither of which can be calculated in closed analytical form but can be calculated numerically. The numerical calculations are carried out to check the validity of the sum rules. The procedure for constructing sum rules for general potentials is discussed. Generalisations of Kramers relations and the Virial theorem are discussed. |
| spellingShingle | Sukumar, C Hierarchy of sum rules for oscillator strengths |
| title | Hierarchy of sum rules for oscillator strengths |
| title_full | Hierarchy of sum rules for oscillator strengths |
| title_fullStr | Hierarchy of sum rules for oscillator strengths |
| title_full_unstemmed | Hierarchy of sum rules for oscillator strengths |
| title_short | Hierarchy of sum rules for oscillator strengths |
| title_sort | hierarchy of sum rules for oscillator strengths |
| work_keys_str_mv | AT sukumarc hierarchyofsumrulesforoscillatorstrengths |