Intermediate Spectral Theory and Quantum Dynamics pdf epub mobi txt 电子书下载 2026

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出版者:

作者:De Oliveira, Cesar R.

出品人:

页数:423

译者:

出版时间:

价格:$ 84.69

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isbn号码:9783764387945

丛书系列:

图书标签:

Spectral Theory
Quantum Dynamics
Quantum Mechanics
Mathematical Physics
Operator Theory
Scattering Theory
Time-Dependent Perturbation Theory
Linear Operators
Functional Analysis
Hilbert Spaces

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具体描述

The spectral theory of linear operators plays a key role in the mathematical formulation of quantum theory. Furthermore, such a rigorous mathematical foundation leads to a more profound insight into the nature of quantum mechanics. This textbook provides a concise and comprehensible introduction to the spectral theory of (unbounded) self-adjoint operators and its application in quantum dynamics. The book places emphasis on the symbiotic relationship of these two domains by (1) presenting the basic mathematics of nonrelativistic quantum mechanics of one particle, i.e., developing the spectral theory of self-adjoint operators in infinite-dimensional Hilbert spaces from the beginning, and (2) giving an overview of many of the basic functional aspects of quantum theory, from its physical principles to the mathematical models. The book is intended for graduate (or advanced undergraduate) students and researchers interested in mathematical physics. It starts with linear operator theory, spectral questions and self-adjointness, and ends with the effect of spectral type on the large time behaviour of quantum systems. Many examples and exercises are included that focus on quantum mechanics.

“Intermediate Spectral Theory and Quantum Dynamics”是一本全面且深入探讨光谱理论与量子动力学交叉领域的学术著作。这本书以严谨的逻辑结构和丰富的理论分析，旨在为读者提供一个系统性的学习框架。内容涵盖了经典和现代数学工具的运用，从线性方程的解与特征值问题，到量子系统的动态演化，再延伸至复杂函数空间与非自反算符的研究。这本书不仅关注理论深度，还注重其实际应用，帮助读者理解如何在不同物理和数学背景下进行建模与分析。作者深入剖析了光谱分析在量子力学中的核心地位，通过详细讲解谐振子、微扰理论及变分法等经典方法，展示这些工具如何帮助求解复杂问题。书中还引入了现代数值计算技术，使读者能够掌握高效的求解策略和算法实现，为处理实际科研问题提供坚实基础。对于希望拓展量子动力学理论的读者来说，这本书是一部必备的参考资料。内容设计兼顾严谨与可读性，章节安排合理，逻辑清晰，每个部分均有充分的例子和问题分析，使得学习过程不单调而富有成效。无论是物理学基础知识较弱的读者，还是已经有一定背景的研究者，这本书都能提供有价值的知识支持和思考方向。作者在整个过程中注重语言的流畅与专业性的平衡，避免过度简化，同时不忘强调数学推导的准确性。这本书不仅是一部理论著作，更是对学习者全面提升理解能力的重要资源。这一书旨在帮助读者建立扎实的数学与物理结合能力，在量子动力学和谱分析领域开创自己的研究路径。通过系统化的学习，读者可以更好地应对复杂问题，并将理论知识转化为实际应用。无论是学生还是科研人员，都可从中获得重要的指导和启示。总体来说，这本书在内容广度、深度与应用性方面均表现突出，成为学术探索的有力工具。