- 量子力学中的教学概念
- - 作者：(加)格斯特松
  - 出版社：世界图书出版公司
  - ISBN：9787510005022
  - 出版日期：2009/08/01
  - 页数：286
- 售价：14

内容大纲
作者介绍
目录
1  Physical Background
  1.1  The Double-Slit Experiment
  1.2  Wave Functions
  1.3  State Space
  1.4  The SchrSdinger Equation
  1.5  Mathematical Supplement: Operators on Hilbert Spaces
2  Dynamics
  2.1  Conservation of Probability
  2.2  Existence of Dynamics
  2.3  The Free Propagator
  2.4  Mathematical Supplement: Operator Adjoints
  2.5  Mathematical Supplement: the Fourier Transform
  2.5.1  Definition of the Fourier Transform
  2.5.2  Properties of the Fourier Transform
  2.5.3  Functions of the Derivative
3  Observables
  3.1  Mean Values and the Momentum Operator
  3.2  Observables
  3.3  The Heisenberg Representation
  3.4  Quantization
  3.5  Pseudodifferential Operators
4  The Uncertainty Principle
  4.1  The Heisenberg Uncertainty Principle
  4.2  A Refined Uncertainty Principle
  4.3  Application: Stability of Hydrogen
5  Spectral Theory
  5.1  The Spectrum of an Operator
  5.2  Functions of Operators and the Spectral Mapping Theorem
  5.3  Applications to Schr6dinger Operators
  5.4  Spectrum and Evolution
  5.5  Variational Characterization of Eigenvalues
  5.6  Number of Bound States
  5.7  Mathematical Supplement: Integral Operators
6  Scattering States
  6.1  Short-range Interactions: ■
  6.2  Long-range Interactions: ■
  6.3  Wave Operators
7  Special Cases
  7.1  The Infinite Well
  7.2  The Torus
  7.3  A Potential Step
  7.4  The Square Well
  7.5  The Harmonic Oscillator
  7.6  A Particle on a Sphere
  7.7  The Hydrogen Atom
  7.8  A Particle in an External EM Field
8  Many-particle Systems
  8.1  Quantization of a Many-particle System
  8.2  Separation of the Centre-of-mass Motion
  8.3  Break-ups

  8.4  The HVZ Theorem
  8.5  Intra- vs. Inter-cluster Motion
  8.6  Existence of Bound States for Atoms and Molecules
  8.7  Scattering States
  8.8  Mathematical Supplement: Tensor Products
  8.9  Appendix: Hartree and Gross-Pitaevski Equations
9  Density Matrices
  9.1  Introduction
  9.2  States and Dynamics
  9.3  Open Systems
  9.4  The Thermodynamic Limit
  9.5  Equilibrium States
  9.6  The T ~ 0 Limit
  9.7  Example: a System of Harmonic Oscillators
  9.8  A Particle Coupled to a Reservoir
  9.9  Quantum Systems
  9.10  Problems
  9.11  Hilbert Space Approach
  9.12  BEC at T=0
  9.13  Appendix: the Ideal Bose Gas
  9.14  Appendix: Bose-Einstein Condensation
  9.15  Mathematical Supplement: the Trace, and Trace Class Operators
  9.16  Mathematical Supplement: Projections
10 Perturbation Theory: Feshbach Method
  10.1  The Feshbach Method
  10.2  Example: The Zeeman Effect
  10.3  Example: Time-dependent Perturbations
  10.4  Appendix: Proof of Theorem 10.1
11  The Feynman Path Integral
  11.1  The Feynman Path Integral
  11.2  Generalizations of the Path Integral
  11.3  Mathematical Supplement: The Trotter
  Product Formula
12  Quasi-classical Analysis
  12.1  Quasi-classical Asymptotics of the Propagator
  12.2  Quasi-classical Asymptotics of Green's Function
  12.2.1  Appendix
  12.3  Bohr-Sommerfeld Semi-classical Quantization
  12.4  Quasi-classical Asymptotics for the Ground State Energy..
  12.5  Mathematical Supplement: Operator Determinants
13 Mathematical Supplement: The Calculus of Variations
  13.1  Functionals
  13.2  The First Variation and Critical Points
  13.3  Constrained Variational Problems
  13.4  The Second Variation
  13.5  Conjugate Points and Jacobi Fields
  13.6  The Action of the Critical Path
  13.7  Appendix: Connection to Geodesics
14  Resonances
  14.1  Tunneling and Resonances

  14.2  The Free Resonance Energy
  14.3  Instantons
  14.4  Positive Temperatures
  14.5  Pre-exponential Factor for the Bounce
  14.6  Contribution of the Zero-mode
  14.7  Bohr-Sommerfeld Quantization for Resonances
15  Introduction to Quantum Field Theory
  15.1  The Place of QFT
  15.1.1  Physical Theories
  15.1.2  The Principle of Minimal Action
  15.2  Klein-Gordon Theory as a Hamiltonian System
  15.2.1  The Legendre Transform
  15.2.2  Hamiltonians
  15.2.3  Poisson Brackets
  15.2.4  Hamilton's Equations
  15.3  Maxwelrs Equations as a Hamiltonian System
  15.4  Quantization of the Klein-Gordon and Maxwell Equations..
  15.4.1  The Quantization Procedure
  15.4.2  Creation and Annihilation Operators
  15.4.3  Wick Ordering
  15.4.4  Quantizing Maxwelrs Equations
  15.5  Fock Space
  15.6  Generalized Free Theory
  15.7  Interactions
  15.8  Quadratic Approximation
  15.8.1  Further Discussion
  15.8.2  A Brief Remark on Many-body Hamiltonians in Second Quantization and the Hartree Approximation .
16  Quantum Electrodynamics of Non-relativistic Particles:The Theory of Radiation
  16.1  The Hamiltonian
  16.2  Perturbation Set-up
  16.3  Results
  16.4  Mathematical Supplements
  16.4.1  Spectral Projections
  16.4.2  Projecting-out Procedure
17  Supplement: Renormalization Group
  17.1  The Decimation Map
  17.2  Relative Bounds
  17.3  Elimination of Particle and High Photon Energy Degrees of Freedom
  17.4  Generalized Normal Form of Operators on Fock Space
  17.5  The Hamiltonian H0(E, z)
  17.6  A Banach Space of Operators
  17.7  Rescaling
  17.8  The Renormalization Map
  17.9  Linearized Flow
  17.10  Central-stable Manifold for RG and Spectra of Hamiltonians.
  17.11  Appendix
18  Comments on Missing Topics, Literature,and Further Reading
References
Index

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作者介绍

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