Lectures on the Mathematics of Quantum Mechanics II: Selected Topics
Lectures on the Mathematics of Quantum Mechanics II: Selected Topics
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量子力学数学讲座II：选题
DOI：
10.2991/978-94-6239-115-4
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发表时间：
2016
期刊：
影响因子：
--
通讯作者：
G. Dell'Antonio
中科院分区：
文献类型：
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作者：
G. Dell'Antonio
第一卷（通论）与大多数教科书不同，它强调数学结构和数学严谨性，同时适应量子力学高级课程第一学期的教学（书的内容是实际授课的课程）。它也不同于量子力学中强调数学方面的极少数文本，因为这本书是以课堂笔记的形式写成的，具有课程中讲课的结构，即问题的介绍，相关点的概述，所需的数学工具，定理，证明。这使得这本书特别有用的自学和讲师在准备第二门课程在量子力学（在第一个基础课程之后）。加上一些小的补充，它也可以作为量子力学数学课程学生的第一门课程的基础。第二部分（选题选择）是一门更高级课程的课堂讲稿，旨在给出与量子力学相关的数学物理几个领域的研究所必需的基本概念，从固态到奇异相互作用，多体理论，半经典分析，量子统计力学。这本书的结构适合第二学期的课程，其中的讲座是为了提供，除了定理和证明，一个更具体的主题的概述和提示的研究方向。在这方面和主题的宽度，第二卷不同于其他专著的量子力学。第二卷可以是有用的学生谁想要有一个基本的准备做研究和教师谁可能想要使用它作为一个基础的介绍选定的主题
The first volume (General Theory) differs from most textbooks as it emphasizes the mathematical structure and mathematical rigor, while being adapted to the teaching the first semester of an advanced course in Quantum Mechanics (the content of the book are the lectures of courses actually delivered.). It differs also from the very few texts in Quantum Mechanics that give emphasis to the mathematical aspects because this book, being written as Lecture Notes, has the structure of lectures delivered in a course, namely introduction of the problem, outline of the relevant points, mathematical tools needed, theorems, proofs. This makes this book particularly useful for self-study and for instructors in the preparation of a second course in Quantum Mechanics (after a first basic course). With some minor additions it can be used also as a basis of a first course in Quantum Mechanics for students in mathematics curricula. The second part (Selected Topics) are lecture notes of a more advanced course aimed at giving the basic notions necessary to do research in several areas of mathematical physics connected with quantum mechanics, from solid state to singular interactions, many body theory, semi-classical analysis, quantum statistical mechanics. The structure of this book is suitable for a second-semester course, in which the lectures are meant to provide, in addition to theorems and proofs, an overview of a more specific subject and hints to the direction of research. In this respect and for the width of subjects this second volume differs from other monographs on Quantum Mechanics. The second volume can be useful for students who want to have a basic preparation for doing research and for instructors who may want to use it as a basis for the presentation of selected topics