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量子力学中的数学方法：Schrödinger算子的应用（影印版）

样章
作者：
Gerald Teschl
定价：
169.00元
ISBN：
978-7-04-055650-6
版面字数：
630.000千字
开本：
16开
全书页数：
暂无
装帧形式：
精装
重点项目：
暂无
出版时间：
2021-03-08
读者对象：
学术著作
一级分类：
自然科学
二级分类：
力学
三级分类：
应用力学
暂无
  • 前辅文
  • Preface
  • Part 0. Preliminaries
    • Chapter 0. A first look at Banach and Hilbert spaces
      • 0.1. Warm up: Metric and topological spaces
      • 0.2. The Banach space of continuous functions
      • 0.3. The geometry of Hilbert spaces
      • 0.4. Completeness
      • 0.5. Bounded operators
      • 0.6. Lebesgue Lp spaces
      • 0.7. Appendix: The uniform boundedness principle
  • Part 1. Mathematical Foundations of Quantum Mechanics
    • Chapter 1. Hilbert spaces
      • 1.1. Hilbert spaces
      • 1.2. Orthonormal bases
      • 1.3. The projection theorem and the Riesz lemma
      • 1.4. Orthogonal sums and tensor products
      • 1.5. The C* algebra of bounded linear operators
      • 1.6. Weak and strong convergence
      • 1.7. Appendix: The Stone–Weierstraß theorem
    • Chapter 2. Self-adjointness and spectrum
      • 2.1. Some quantum mechanics
      • 2.2. Self-adjoint operators
      • 2.3. Quadratic forms and the Friedrichs extension
      • 2.4. Resolvents and spectra
      • 2.5. Orthogonal sums of operators
      • 2.6. Self-adjoint extensions
      • 2.7. Appendix: Absolutely continuous functions
    • Chapter 3. The spectral theorem
      • 3.1. The spectral theorem
      • 3.2. More on Borel measures
      • 3.3. Spectral types
      • 3.4. Appendix: Herglotz–Nevanlinna functions
    • Chapter 4. Applications of the spectral theorem
      • 4.1. Integral formulas
      • 4.2. Commuting operators
      • 4.3. Polar decomposition
      • 4.4. The min-max theorem
      • 4.5. Estimating eigenspaces
      • 4.6. Tensor products of operators
    • Chapter 5. Quantum dynamics
      • 5.1. The time evolution and Stone’s theorem
      • 5.2. The RAGE theorem
      • 5.3. The Trotter product formula
    • Chapter 6. Perturbation theory for self-adjoint operators
      • 6.1. Relatively bounded operators and the Kato–Rellich theorem
      • 6.2. More on compact operators
      • 6.3. Hilbert–Schmidt and trace class operators
      • 6.4. Relatively compact operators and Weyl’s theorem
      • 6.5. Relatively form-bounded operators and the KLMN theorem
      • 6.6. Strong and norm resolvent convergence
  • Part 2. Schrödinger Operators
    • Chapter 7. The free Schrödinger operator
      • 7.1. The Fourier transform
      • 7.2. Sobolev spaces
      • 7.3. The free Schrödinger operator
      • 7.4. The time evolution in the free case
      • 7.5. The resolvent and Green’s function
    • Chapter 8. Algebraic methods
      • 8.1. Position and momentum
      • 8.2. Angular momentum
      • 8.3. The harmonic oscillator
      • 8.4. Abstract commutation
    • Chapter 9. One-dimensional Schrödinger operators
      • 9.1. Sturm–Liouville operators
      • 9.2. Weyl’s limit circle, limit point alternative
      • 9.3. Spectral transformations I
      • 9.4. Inverse spectral theory
      • 9.5. Absolutely continuous spectrum
      • 9.6. Spectral transformations II
      • 9.7. The spectra of one-dimensional Schrödinger operators
    • Chapter 10. One-particle Schrödinger operators
      • 10.1. Self-adjointness and spectrum
      • 10.2. The hydrogen atom
      • 10.3. Angular momentum
      • 10.4. The eigenvalues of the hydrogen atom
      • 10.5. Nondegeneracy of the ground state
    • Chapter 11. Atomic Schrödinger operators
      • 11.1. Self-adjointness
      • 11.2. The HVZ theorem
    • Chapter 12. Scattering theory
      • 12.1. Abstract theory
      • 12.2. Incoming and outgoing states
      • 12.3. Schrödinger operators with short range potentials
  • Part 3. Appendix
    • Appendix A. Almost everything about Lebesgue integration
      • A.1. Borel measures in a nutshell
      • A.2. Extending a premeasure to a measure
      • A.3. Measurable functions
      • A.4. How wild are measurable objects?
      • A.5. Integration—Sum me up, Henri
      • A.6. Product measures
      • A.7. Transformation of measures and integrals
      • A.8. Vague convergence of measures
      • A.9. Decomposition of measures
      • A.10. Derivatives of measures
  • Bibliographical notes
  • Bibliography
  • Glossary of notation
  • Index

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