| 書目名稱 | Spectral Measures and Dynamics: Typical Behaviors | | 編輯 | Moacir Aloisio,Silas L. Carvalho,César R. de Olive | | 視頻video | http://file.papertrans.cn/874/873833/873833.mp4 | | 概述 | Gathers generic results of spectral measures of importance to the mathematical theory of quantum mechanics.Starts with classical topics, progressing to advanced material developed by the authors.Of sp | | 叢書名稱 | Latin American Mathematics Series | | 圖書封面 |  | | 描述 | This book convenes and deepens generic results about spectral measures, many of them available so far in scattered literature. It starts with classic topics such as Wiener lemma, Strichartz inequality, and the basics of fractal dimensions of measures, progressing to more advanced material, some of them developed by the own authors..A fundamental concept to the mathematical theory of quantum mechanics, the spectral measure relates to the components of the quantum state concerning the energy levels of the Hamiltonian operator and, on the other hand, to the dynamics of such state. However, these correspondences are not immediate, with many nuances and subtleties discovered in recent years..A valuable example of such subtleties is found in the so-called “Wonderland theorem” first published by B. Simon in 1995. It shows that, for some metric space of self-adjoint operators, the set of operators whose spectral measures are singularcontinuous is a generic set (which, for some, is exotic). Recent works have revealed that, on top of singular continuity, there are other generic properties of spectral measures. These properties are usually associated with a number of different notions of gene | | 出版日期 | Book 2023 | | 關(guān)鍵詞 | mathematical physics; quantum mechanics; quantum theory; spectral analysis; elliptic equations; classical | | 版次 | 1 | | doi | https://doi.org/10.1007/978-3-031-38289-5 | | isbn_softcover | 978-3-031-38291-8 | | isbn_ebook | 978-3-031-38289-5Series ISSN 2524-6755 Series E-ISSN 2524-6763 | | issn_series | 2524-6755 | | copyright | The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerl |
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