Preface |
Acknowledgments |
A Message to the Reader |
List of Symbols |
One-Dimensional Motion / Chapter 1.: |
Position / 1.1.: |
Mathematical Expectation / 1.2.: |
Momentum / 1.3.: |
Energy / 1.4.: |
Observables / 1.5.: |
Operators / 1.6.: |
Functions of Observables / 1.7.: |
Self-Adjoint Operators / 1.8.: |
Hilbert Space / 1.9.: |
The Spectral Theorem / 1.10.: |
Exercises |
The Spectrum / Chapter 2.: |
The Resolvent / 2.1.: |
Finding the Spectrum / 2.2.: |
The Position Operator / 2.3.: |
The Momentum Operator / 2.4.: |
The Energy Operator / 2.5.: |
The Potential / 2.6.: |
A Class of Functions / 2.7.: |
The Spectrum of H / 2.8.: |
The Essential Spectrum / Chapter 3.: |
An Example / 3.1.: |
A Calculation / 3.2.: |
Finding the Eigenvalues / 3.3.: |
The Domain of H / 3.4.: |
Back to Hilbert Space / 3.5.: |
Compact Operators / 3.6.: |
Relative Compactness / 3.7.: |
Proof of Theorem 3.7.5 / 3.8.: |
The Negative Eigenvalues / Chapter 4.: |
The Possibilities / 4.1.: |
Forms Extensions / 4.2.: |
The Remaining Proofs / 4.3.: |
Negative Eigenvalues / 4.4.: |
Existence of Bound States / 4.5.: |
Existence of Infinitely Many Bound States / 4.6.: |
Existence of Only a Finite Number of Bound States / 4.7.: |
Another Criterion / 4.8.: |
Estimating the Spectrum / Chapter 5.: |
Introduction / 5.1.: |
Some Crucial Lemmas / 5.2.: |
A Lower Bound for the Spectrum / 5.3.: |
Lower Bounds for the Essential Spectrum / 5.4.: |
An Inequality / 5.5.: |
Bilinear Forms / 5.6.: |
Intervals Containing the Essential Spectrum / 5.7.: |
Coincidence of the Essential Spectrum with an Interval / 5.8.: |
The Harmonic Oscillator / 5.9.: |
The Morse Potential / 5.10.: |
Scattering Theory / Chapter 6.: |
Time Dependence / 6.1.: |
Scattering States / 6.2.: |
Properties of the Wave Operators / 6.3.: |
The Domains of the Wave Operators / 6.4.: |
Local Singularities / 6.5.: |
Long-Range Potentials / Chapter 7.: |
The Coulomb Potential / 7.1.: |
Some Examples / 7.2.: |
The Estimates / 7.3.: |
The Derivatives of V(x) / 7.4.: |
The Relationship Between X[subscript t] and V(x) / 7.5.: |
An Identity / 7.6.: |
The Reduction / 7.7.: |
Mollifiers / 7.8.: |
Time-Independent Theory / Chapter 8.: |
The Resolvent Method / 8.1.: |
The Theory / 8.2.: |
A Simple Criterion / 8.3.: |
The Application / 8.4.: |
Completeness / Chapter 9.: |
Definition / 9.1.: |
The Abstract Theory / 9.2.: |
Some Identities / 9.3.: |
Another Form / 9.4.: |
The Unperturbed Resolvent Operator / 9.5.: |
The Perturbed Operator / 9.6.: |
Analytic Dependence / 9.7.: |
Projections / 9.9.: |
An Analytic Function Theorem / 9.10.: |
The Combined Results / 9.11.: |
Absolute Continuity / 9.12.: |
The Intertwining Relations / 9.13.: |
Strong Completeness / 9.14.: |
The More Difficult Problem / 10.1.: |
The Technique / 10.2.: |
Verification for the Hamiltonian / 10.4.: |
An Extension / 10.5.: |
The Principle of Limiting Absorption / 10.6.: |
Oscillating Potentials / Chapter 11.: |
A Surprise / 11.1.: |
The Hamiltonian / 11.2.: |
A Variation / 11.3.: |
Examples / 11.5.: |
Eigenfunction Expansions / Chapter 12.: |
The Usefulness / 12.1.: |
The Problem / 12.2.: |
Operators on L[superscript p] / 12.3.: |
Weighted L[superscript p]-Spaces / 12.4.: |
Extended Resolvents / 12.5.: |
The Formulas / 12.6.: |
Some Consequences / 12.7.: |
Summary / 12.8.: |
Restricted Particles / Chapter 13.: |
A Particle Between Walls / 13.1.: |
The Energy Levels / 13.2.: |
Compact Resolvents / 13.3.: |
One Opaque Wall / 13.4.: |
Scattering on a Half-Line / 13.5.: |
The Spectral Resolution for the Free Particle on a Half-Line / 13.6.: |
Hard-Core Potentials / Chapter 14.: |
Local Absorption / 14.1.: |
The Modified Hamiltonian / 14.2.: |
The Resolvent Operator for H[subscript 1] / 14.3.: |
The Wave Operators W[subscript plus or minus] (H[subscript 1] H[subscript 0]) / 14.4.: |
Propagation / 14.5.: |
Proof of Theorem 14.5.1 / 14.6.: |
Completeness of the Wave Operators W[subscript plus or minus], (H[subscript 1] H[subscript 0]) / 14.7.: |
The Wave Operators W[subscript plus or minus] (H, H[subscript 1]) / 14.8.: |
A Regularity Theorem / 14.9.: |
A Family of Spaces / 14.10.: |
The Invariance Principle / Chapter 15.: |
A Simple Result / 15.1.: |
Trace Class Operators / 15.3.: |
The Abstract Theorem / 16.1.: |
Hilbert--Schmidt Operators / 16.2.: |
The Fourier Transform / 16.4.: |
Exercises A |
Exercises B / Appendix B.: |
Holder's Inequality and Banach Space / Appendix C.: |
Bibliography |
Index |
Preface |
Acknowledgments |
A Message to the Reader |
List of Symbols |
One-Dimensional Motion / Chapter 1.: |
Position / 1.1.: |