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