Operator methods in quantum mechanics

>> Google Books

QR code for holdings

Operator methods in quantum mechanics / Martin Schechter

Format:: Book
Published:: New York : North Holland, c1981
Description:: xx, 324 p. ; 24 cm
Authors:: Schechter, Martin <DA0067015X>
ISBN:: 9780444004109 [0444004106]
NCID:: BA01499901

Holding items in this series

Full Text

Holdings

Other editions or volumes

Bibliography Details

Note:

Bibliography: p. [319]-321
Includes index

Subject:

Operator theory; Quantum theory

Language:

English

Table of Contents:

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