Tabla de contenidos provista por Syndetics

• Preface(p. xiii)
• Acknowledgments(p. xv)
• A Message to the Reader(p. xvii)
• List of Symbols(p. xix)
• Chapter 1. One-Dimensional Motion(p. 1)
• 1.1. Position(p. 1)
• 1.2. Mathematical Expectation(p. 2)
• 1.3. Momentum(p. 5)
• 1.4. Energy(p. 7)
• 1.5. Observables(p. 8)
• 1.6. Operators(p. 11)
• 1.7. Functions of Observables(p. 13)
• 1.8. Self-Adjoint Operators(p. 17)
• 1.9. Hilbert Space(p. 20)
• 1.10. The Spectral Theorem(p. 23)
• Exercises(p. 25)
• Chapter 2. The Spectrum(p. 26)
• 2.1. The Resolvent(p. 26)
• 2.2. Finding the Spectrum(p. 28)
• 2.3. The Position Operator(p. 29)
• 2.4. The Momentum Operator(p. 30)
• 2.5. The Energy Operator(p. 32)
• 2.6. The Potential(p. 33)
• 2.7. A Class of Functions(p. 35)
• 2.8. The Spectrum of H(p. 39)
• Exercises(p. 39)
• Chapter 3. The Essential Spectrum(p. 40)
• 3.1. An Example(p. 40)
• 3.2. A Calculation(p. 42)
• 3.3. Finding the Eigenvalues(p. 43)
• 3.4. The Domain of H(p. 45)
• 3.5. Back to Hilbert Space(p. 46)
• 3.6. Compact Operators(p. 48)
• 3.7. Relative Compactness(p. 51)
• 3.8. Proof of Theorem 3.7.5(p. 54)
• Exercises(p. 57)
• Chapter 4. The Negative Eigenvalues(p. 59)
• 4.1. The Possibilities(p. 59)
• 4.2. Forms Extensions(p. 60)
• 4.3. The Remaining Proofs(p. 64)
• 4.4. Negative Eigenvalues(p. 66)
• 4.5. Existence of Bound States(p. 68)
• 4.6. Existence of Infinitely Many Bound States(p. 69)
• 4.7. Existence of Only a Finite Number of Bound States(p. 73)
• 4.8. Another Criterion(p. 77)
• Exercises(p. 78)
• Chapter 5. Estimating the Spectrum(p. 79)
• 5.1. Introduction(p. 79)
• 5.2. Some Crucial Lemmas(p. 79)
• 5.3. A Lower Bound for the Spectrum(p. 82)
• 5.4. Lower Bounds for the Essential Spectrum(p. 83)
• 5.5. An Inequality(p. 86)
• 5.6. Bilinear Forms(p. 89)
• 5.7. Intervals Containing the Essential Spectrum(p. 94)
• 5.8. Coincidence of the Essential Spectrum with an Interval(p. 96)
• 5.9. The Harmonic Oscillator(p. 98)
• 5.10. The Morse Potential(p. 100)
• Exercises(p. 101)
• Chapter 6. Scattering Theory(p. 103)
• 6.1. Time Dependence(p. 103)
• 6.2. Scattering States(p. 105)
• 6.3. Properties of the Wave Operators(p. 108)
• 6.4. The Domains of the Wave Operators(p. 112)
• 6.5. Local Singularities(p. 115)
• Exercises(p. 117)
• Chapter 7. Long-Range Potentials(p. 118)
• 7.1. The Coulomb Potential(p. 118)
• 7.2. Some Examples(p. 120)
• 7.3. The Estimates(p. 121)
• 7.4. The Derivatives of V(x)(p. 124)
• 7.5. The Relationship Between X[subscript t] and V(x)(p. 127)
• 7.6. An Identity(p. 128)
• 7.7. The Reduction(p. 129)
• 7.8. Mollifiers(p. 131)
• Exercises(p. 136)
• Chapter 8. Time-Independent Theory(p. 137)
• 8.1. The Resolvent Method(p. 137)
• 8.2. The Theory(p. 139)
• 8.3. A Simple Criterion(p. 143)
• 8.4. The Application(p. 146)
• Exercises(p. 150)
• Chapter 9. Completeness(p. 151)
• 9.1. Definition(p. 151)
• 9.2. The Abstract Theory(p. 153)
• 9.3. Some Identities(p. 154)
• 9.4. Another Form(p. 157)
• 9.5. The Unperturbed Resolvent Operator(p. 159)
• 9.6. The Perturbed Operator(p. 163)
• 9.7. Compact Operators(p. 165)
• 9.8. Analytic Dependence(p. 168)
• 9.9. Projections(p. 171)
• 9.10. An Analytic Function Theorem(p. 173)
• 9.11. The Combined Results(p. 177)
• 9.12. Absolute Continuity(p. 180)
• 9.13. The Intertwining Relations(p. 182)
• 9.14. The Application(p. 183)
• Exercises(p. 187)
• Chapter 10. Strong Completeness(p. 190)
• 10.1. The More Difficult Problem(p. 190)
• 10.2. The Abstract Theory(p. 191)
• 10.3. The Technique(p. 192)
• 10.4. Verification for the Hamiltonian(p. 195)
• 10.5. An Extension(p. 200)
• 10.6. The Principle of Limiting Absorption(p. 205)
• Exercises(p. 207)
• Chapter 11. Oscillating Potentials(p. 208)
• 11.1. A Surprise(p. 208)
• 11.2. The Hamiltonian(p. 209)
• 11.3. The Estimates(p. 211)
• 11.4. A Variation(p. 212)
• 11.5. Examples(p. 214)
• Exercises(p. 215)
• Chapter 12. Eigenfunction Expansions(p. 217)
• 12.1. The Usefulness(p. 217)
• 12.2. The Problem(p. 218)
• 12.3. Operators on L[superscript p](p. 219)
• 12.4. Weighted L[superscript p]-Spaces(p. 220)
• 12.5. Extended Resolvents(p. 223)
• 12.6. The Formulas(p. 225)
• 12.7. Some Consequences(p. 229)
• 12.8. Summary(p. 232)
• Exercises(p. 233)
• Chapter 13. Restricted Particles(p. 234)
• 13.1. A Particle Between Walls(p. 234)
• 13.2. The Energy Levels(p. 239)
• 13.3. Compact Resolvents(p. 241)
• 13.4. One Opaque Wall(p. 243)
• 13.5. Scattering on a Half-Line(p. 245)
• 13.6. The Spectral Resolution for the Free Particle on a Half-Line(p. 250)
• Exercises(p. 252)
• Chapter 14. Hard-Core Potentials(p. 254)
• 14.1. Local Absorption(p. 254)
• 14.2. The Modified Hamiltonian(p. 256)
• 14.3. The Resolvent Operator for H[subscript 1](p. 257)
• 14.4. The Wave Operators W[subscript plus or minus] (H[subscript 1] H[subscript 0])(p. 261)
• 14.5. Propagation(p. 262)
• 14.6. Proof of Theorem 14.5.1(p. 265)
• 14.7. Completeness of the Wave Operators W[subscript plus or minus], (H[subscript 1] H[subscript 0])(p. 267)
• 14.8. The Wave Operators W[subscript plus or minus] (H, H[subscript 1])(p. 269)
• 14.9. A Regularity Theorem(p. 272)
• 14.10. A Family of Spaces(p. 275)
• Exercises(p. 280)
• Chapter 15. The Invariance Principle(p. 282)
• 15.1. Introduction(p. 282)
• 15.2. A Simple Result(p. 282)
• 15.3. The Estimates(p. 287)
• 15.4. An Extension(p. 287)
• 15.5. Another Form(p. 292)
• Exercises(p. 295)
• Chapter 16. Trace Class Operators(p. 296)
• 16.1. The Abstract Theorem(p. 296)
• 16.2. Some Consequences(p. 299)
• 16.3. Hilbert--Schmidt Operators(p. 301)
• 16.4. Verification for the Hamiltonian(p. 303)
• Exercises(p. 304)
• Appendix A. The Fourier Transform(p. 305)
• Exercises A(p. 308)
• Appendix B. Hilbert Space(p. 309)
• Exercises B(p. 315)
• Appendix C. Holder's Inequality and Banach Space(p. 316)
• Bibliography(p. 319)
• Index(p. 323)