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解析学火曜セミナー
過去の記録 ～04/17｜次回の予定｜今後の予定 04/18～
| 開催情報 | 火曜日 16:00～17:30 数理科学研究科棟(駒場) 156号室 |
|---|---|
| 担当者 | 石毛 和弘, 坂井 秀隆, 伊藤 健一 |
| セミナーURL | https://www.ms.u-tokyo.ac.jp/seminar/analysis/ |
2019年11月26日(火)
16:50-18:20 数理科学研究科棟(駒場) 128号室
蘆田聡平 氏 (学習院大学)
Accurate lower bounds for eigenvalues of electronic Hamiltonians (Japanese)
蘆田聡平 氏 (学習院大学)
Accurate lower bounds for eigenvalues of electronic Hamiltonians (Japanese)
[ 講演概要 ]
Electronic Hamiltonians are differential operators depending on relative positions of nuclei as parameters. When we regard an eigenvalues of an electronic Hamiltonian as a function of relative positions of nuclei, minimum points correspond to shapes of molecules. Upper bounds for eigenvalues are obtained by variational methods. However, since the physical information as minimum points does not change when a reference point of energy changes, physical information can not be obtained by variational methods only. Combining lower and upper bounds physical information is obtained.
In this talk we discuss the Weinstein-Arnszajn intermediate problem methods for lower bounds of eigenvalues based on comparison of operators. A method for lower bounds of one-electronic Hamiltonians is also introduced. Some computations for two kinds of hydrogen molecule-ion are shown.
Electronic Hamiltonians are differential operators depending on relative positions of nuclei as parameters. When we regard an eigenvalues of an electronic Hamiltonian as a function of relative positions of nuclei, minimum points correspond to shapes of molecules. Upper bounds for eigenvalues are obtained by variational methods. However, since the physical information as minimum points does not change when a reference point of energy changes, physical information can not be obtained by variational methods only. Combining lower and upper bounds physical information is obtained.
In this talk we discuss the Weinstein-Arnszajn intermediate problem methods for lower bounds of eigenvalues based on comparison of operators. A method for lower bounds of one-electronic Hamiltonians is also introduced. Some computations for two kinds of hydrogen molecule-ion are shown.
