《數學家用的量子理論》是2016年世界圖書出版公司出版的著作，作者是 Brian C. Hall。
基本介紹
- 中文名：《數學家用的量子理論》
- 作者：Brian C. Hall
- 出版時間：2016年9月1日
- 出版社：世界圖書出版公司
- ISBN：9787519203238
內容簡介,作者簡介,目錄,
內容簡介
儘管量子物理思想在現代數學的許多領域發揮著重要的作用，但是針對數學家的量子力學書卻幾乎沒有。該書用數學家熟悉的語言介紹了量子力學的主要思想。接觸物理少的讀者在會比較喜歡該書用會話的語調來講述諸如用Hibert空間法研究量子理論、一維空間的薛丁格方程、有界無界自伴運算元的譜定理、Ston-von Neumann定理、Wentzel-Kramers-Brillouin逼近、李群和李代數量子力學中的作用等。
作者簡介
Brian C. Hall（B.C. 霍爾，美國）是國際知名學者，在數學界享有盛譽。本書凝聚了作者多年科研和教學成果，適用於科研工作者、高校教師和研究生。
目錄
1 The Experimental Origins of Quantum Mechanics
1.1 Is Light a Wave or a Particle
1.2 Is an Electron a Wave or a Particle
1.3 SchrSdinger and Heisenberg
1.4 A Matter of Interpretation
1.5 Exercises
2 A First Approach to Classical Mechanics
2.1 Motion in R1
2.2 Motion in Rn
2.3 Systems of Particles
2.4 Angular Momentum
2.5 Poisson Brackets and Hamiltonian Mechanics
2.6 The Kepler Problem and the Runge-Lenz Vector
2.7 Exercises
3 A First Approach to Quantum Mechanics
3.1 Waves, Particles, and Probabilities
3.2 A Few Words About Operators and Their Adjoints
3.3 Position and the Position Operator
3.4 Momentum and the Momentum Operator
3.5 The Position and Momentum Operators
3.6 Axioms of Quantum Mechanics: Operators and Measurements
3.7 Time-Evolution in Quantum Theory
3.8 The Heisenberg Picture
3.9 Example: A Particle in a Box
3.10 Quantum Mechanics for a Particle in Rn
3.11 Systems of Multiple Particles
3.12 Physics Notation
3.13 Exercises
4 The Free Schrodinger Equation
4.1 Solution by Means of the Fourier Transform
4.2 Solution as a Convolution
4.3 Propagation of the Wave Packet: First Approach
4.4 Propagation of the Wave Packet: Second Approach
4.5 Spread of the Wave Packet
4.6 Exercises
5 A Particle in a Square Well
5.1 The Time-Independent SchrSdinger Equation
5.2 Domain Questions and the Matching Conditions
5.3 Finding Square-Integrable Solutions
5.4 Tunneling and the Classically Forbidden Region
5.5 Discrete and Continuous Spectrum
5.6 Exercises
6 Perspectives on the Spectral Theorem
6.1 The Difficulties with the Infinite-Dimensional Case
6.2 The Goals of Spectral Theory
6.3 A Guide to Reading
6.4 The Position Operator
6.5 Multiplication Operators
6.6 The Momentum Operator
7 The Spectral Theorem for Bounded Self-Adjoint Operators: Statements
7.1 Elementary Properties of Bounded Operators
7.2 Spectral Theorem for Bounded Self-Adjoint Operators, I
7.3 Spectral Theorem for Bounded Self-Adjoint Operators, II
7.4 Exercises
8 The Spectral Theorem for Bounded Self-Adjoint Operators: Proofs
8.1 Proof of the Spectral Theorem, First Version
8.2 Proof of the Spectral Theorem, Second Version
8.3 Exercises
9 Unbounded Self-Adjoint Operators
9.1 Introduction
9.2. Adjoint and Closure of an Unbounded Operator
9.3 Elementary Properties of Adjoints and Closed Operators
9.4 The Spectrum of an Unbounded Operator
9.5 Conditions for Self-Adjointness and Essential Self-Adjointness
9.6 A Counterexample
9.7 An Example
9.8 The Basic Operators of Quantum Mechanics
9.9 Sums of Self-Adjoint Operators
9.10 Another Counterexample
9.11 Exercises
10 The Spectral Theorem for Unbounded Self-Adjoint Operators
10.1 Statements of the Spectral Theorem
10.2 Stone's Theorem and One-Parameter Unitary Groups
10.3 The Spectral Theorem for Bounded Normal Operators
10.4 Proof of the Spectral Theorem for Unbounded Self-Adjoint Operators
10.5 Exercises
