数学家用的量子理论英文版【正版保证】 下载 pdf 百度网盘 epub 免费 2025 电子版 mobi 在线

尽管量子物理思想在现代数学的许多领域发挥着重要的作用，但是针对数学家的量子力学书却几乎没有。该书用数学家熟悉的语言介绍了量子力学的主要思想。接触物理少的读者在会比较喜欢该书用会话的语调来讲述诸如用Hibert空间法研究量子理论、一维空间的薛定谔方程、有界无界自伴算子的谱定理、Ston-von Neumann定理、Wentzel-Kramers-Brillouin逼近、李群和李代数量子力学中的作用等

1 The Experimental Origins of Quantum Mechanics

1．1 Is Light a Wave or a Particle?

1．2 Is aElectroa 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 MotioiR1

2．2 MotioiRn

2．3 Systems of Particles

2．4 Angular Momentum

2．5 PoissoBrackets and HamiltoniaMechanics

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 Positioand the PositioOperator

3．4 Momentum and the Momentum Operator

3．5 The Positioand Momentum Operators

3．6 Aoms of Quantum Mechanics： Operators and Measurements

3．7 Time-EvolutioiQuantum Theory

3．8 The Heisenberg Picture

3．9 Example： A Particle ia Box

3．10 Quantum Mechanics for a Particle iRn

3．11 Systems of Multiple Particles

3．12 Physics Notation

3．13 Exercises

4 The Free Schrodinger Equation

4．1 Solutioby Means of the Fourier Transform

4．2 Solutioas a Convolution

4．3 Propagatioof the Wave Packet： First Approach

4．4 Propagatioof the Wave Packet： Second Approach

4．5 Spread of the Wave Packet

4．6 Exercises

5 A Particle ia Square Well

5．1 The Time-Independent SchrSdinger Equation

5．2 DomaiQuestions and the Matching Conditions

5．3 Finding Square-Integrable Solutions

5．4 Tunneling and the Classically ForbiddeRegion

5．5 Discrete and Continuous Spectrum

5．6 Exercises

6 Perspectives othe 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 PositioOperator

6．5 MultiplicatioOperators

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 aUnbounded Operator

9．3 Elementary Properties of Adjoints and Closed Operators

9．4 The Spectrum of aUnbounded Operator

9．5 Conditions for Self-Adjointness and Essential Self-Adjointness

9．6 A Counterexample

9．7 AExample

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

11 The Harmonic Oscillator

11．1 The Role of the Harmonic Oscillator

11．2 The Algebraic Approach

11．3 The Analytic Approach

11．4 DomaiConditions and Completeness

11．5 Exercises

12 The Uncertainty Principle

12．1 Uncertainty Principle， First Version

12．2 A Counterexample

12．3 Uncertainty Principle， Second Version

12．4 Minimum Uncertainty States

12．5 Exercises

13 QuantizatioSchemes for EuclideaSpace

13．1 Ordering Ambiguities

13．2 Some CommoQuantizatioSchemes

13．3 The Weyl Quantizatiofor R2n

13．4 The "No Go" Theorem of Groenewold

13．5 Exercises

14 The Stone-yoNeumanTheorem

14．1 A Heuristic Argument

14．2 The Exponentiated CommutatioRelations

14．3 The Theorem

14．4 The Segal-BargmanSpace

14．5 Exercises

15 The WKB Appromation

15．1 Introduction

15．2 The Old Quantum Theory and the Bohr-Sommerfeld Condition

15．3 Classical and Semiclassical Appromations

15．4 The WKB AppromatioAway from the Turning Points

15．5 The Airy Functioand the ConnectioFormulas

15．6 A Rigorous Error Estimate

15．7 Other Approaches

15．8 Exercises

16 Lie Groups， Lie Algebras， and Representations

16．1 Summary

16．2 Matrix Lie Groups

16．3 Lie Algebras

16．4 The Matrix Exponential

16．5 The Lie Algebra of a Matrix Lie Group

16．6 Relationships BetweeLie Groups and Lie Algebras

16．7 Finite-Dimensional Representations of Lie Groups and Lie Algebras

16．8 New Representations from Old

16．9 Infinite-Dimensional Unitary Representations

16．10 Exercises

17 Angular Momentum and Spin

17．1 The Role of Angular Momentum iQuantum Mechanics

17．2 TheAngular Momentum Operators iR3

17．3 Angular Momentum from the Lie Algebra Point of View

17．4 The Irreducible Representations of so(3)

17．5 The Irreducible Representations of S0(3)

17．6 Realizing the Representations Inside L2(S2)

17．7 Realizing the Representations Inside L2(~3)

17．8 Spin

17．9 Tensor Products of Representations： "Additioof Angular Momentum"

17．10 Vectors and Vector Operators

17．11 Exercises

18 Radial Potentials and the HydrogeAtom

18．1 Radial Potentials

18．2 The HydrogeAtom： Preliminaries

18．3 The Bound States of the HydrogeAtom

18．4 The Runge-Lenz Vector ithe Quantum Kepler Problem

18．5 The Role of Spin

18．6 Runge-Lenz Calculations

18．7 Exercises

19 Systems and Subsystems， Multiple Particles

19．1 Introduction

19．2 Trace-Class and Hilbert Schmidt Operators

19．3 Density Matrices： The General Notioof the State of a Quantum System

19．4 Modified Aoms for Quantum Mechanics

19．5 Composite Systems and the Tensor Product

19．6 Multiple Particles： Bosons and Fermions

19．7 "Statistics" and the Pauli ExclusioPrinciple

19．8 Exercises

20 The Path Integral Formulatioof Quantum Mechanics

20．1 Trotter Product Formula

20．2 Formal Derivatioof the FeynmaPath Integral

20．3 The Imaginary-Time Calculation

20．4 The Wiener Measure

20．5 The Feynman-Kac Formula

20．6 Path Integrals iQuantum Field Theory

20．7 Exercises

21 HamiltoniaMechanics oManifolds

21．1 Calculus oManifolds

21．2 Mechanics oSymplectic Manifolds

21．3 Exercises

22 Geometric QuantizatiooEuclideaSpace

22．1 Introduction

22．2 Prequantization

22．3 Problems with Prequantization

22．4 Quantization

22．5 Quantizatioof Observables

22．6 Exercises

23 Geometric QuantizatiooManifolds

23．1 Introduction

23．2 Line Bundles and Connections

23．3 Prequantization

23．4 Polarizations

23．5 QuantizatioWithout Half-Forms

23．6 Quantizatiowith Half-Forms： The Real Case

23．7 Quantizatiowith Half-Forms： The Complex Case

23．8 Pairing Maps

23．9 Exercises

A Review of Basic Material

A．1 Tensor Products of Vector Spaces

A．2 Measure Theory

A．3 Elementary Fumctional Analysis

A．4 Hilbert Spaces and Operators oThem

References

Index

Brian C. Hall(B.C. 霍尔，美国）是国际知名学者，在数学界享有盛誉。本书凝聚了作者多年科研和教学成果，适用于科研工作者、高校教师和研究生。

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