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＜図書＞
Lagrangian analysis and quantum mechanics : a mathematical structure related to asymptotic expansions and the Maslov index
| 責任表示 | Jean Leray ; English translation by Carolyn Schroeder |
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| データ種別 | 図書 |
| 出版者 | Cambridge, Mass. : MIT Press |
| 出版年 | c1981 |
| 本文言語 | 英語 |
| 大きさ | xvi, 271 p. ; 24 cm |
| 概要 | This work might have been entitled The Introduction of Planck's Constant into Mathematics, in that it introduces quantum conditions in a purely mathematical way in order to remove the singularities th...t arise in obtaining approximations to solutions of complex differential equations. The book's first chapter develops the necessary mathematical apparatus: Fourier transforms, metaplectic and symplectic groups, the Maslov index, and lagrangian varieties. The second chapter orders Maslov's conceptions in a manner that avoids contraditions and creates step by step an essentially new structure-the lagrangian ayalysis. Unexpectedly and strangely the last step requires the datum of a constant, which in applications to quantum mechanics is identified with Planck's constant. The final two chapters apply lagrangian analysis directly to the Schr÷dinger, the Klein-Gordon, and the Dirac equations. Magnetic field effects and even the Paschen-Back effect are taken into account. Jean Leray-who has been professor at the CollFge de France for the past thirty years-has made fundamental contributions to theoretical hydrodynamics, to the study of elliptic, hyperbolic, and analytic linear and nonlinear equations, and to algebraic topology and its applications to analysis. His motivations always had their origin in physical problems, except during World War II: As a prisoner of war in Germany for five years, he concealed his interest in mathematical applications by making fruitful investigations in the field of pure algebraic topology. 続きを見る |
所蔵情報
| 状態 | 巻次 | 所蔵場所 | 請求記号 | 刷年 | 文庫名称 | 資料番号 | コメント | 予約・取寄 | 複写申込 | 自動書庫 |
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【故障中】理系図 自動書庫 | 104/LER | 1981 |
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068252182001773 |
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数理 関数構造 | LERA/10/2 |
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068222182001972 |
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書誌詳細
| 一般注記 | Bibliography: p. [269]-271 |
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| 著者標目 | *Leray, Jean, 1906-1998 |
| 件 名 | LCSH:Differential equations, Partial -- Asymptotic theory
全ての件名で検索
LCSH:Lagrangian functions LCSH:Maslov index LCSH:Quantum theory |
| 分 類 | LCC:QA377 DC19:515.3/53 |
| 書誌ID | 1000913928 |
| ISBN | 0262120879 |
| NCID | BA01395021 |
| 巻冊次 | ISBN:0262120879 |
| 登録日 | 2009.09.16 |
| 更新日 | 2009.09.17 |