دانلود کتاب Scattering Theory: Quantum Theory on Nonrelativistic Collisions

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Preface
Contents
Introduction
1 Mathematical Preliminaries
1-a The Hilbert Space of State Vectors
1-b Subspace
1-c Operators and Inverses
1-d Unitary Operators
1-e Isometric Operators
1-f Convergence of Vectors
1-g Operator limits
2 The Scattering Operator for a Single Particle
2-a Classical Scattering
2-b Quantum Scattering
2-c The Asymptotic Condition
2-d Orthogonality and Asymptotic Completeness
2-e The Scattering Operator
2-f Unitarity
3 Cross Sections in Terms of the S Matrix
3-a Conservation of Energy
3-b The On-Shell T Matrix and Scattering Amplitude
3-c The Classical Cross Section
3-d Definition of the Quantum Cross Section
3-e Calculation of the Quantum Cross Section
3-f The Optical Theorem
4 Scattering of Two Spinless Particles
4-a Two-Particle Wave Functions
4-b The Two-Particle S Operator
4-c Conservation of Energy-Momentum and the T Matrix
4-d Cross Sections in Various Frames
4-e The Center-of-Mass Cross Section
5 Scattering of Two Particles with Spin
5-a The Hilbert Space for Particles with Spin
5-b The S Operator for Particles with Spin
5-c The Amplitudes and Amplitude Matrix
5-d Sums and Averages Over Spins
5-e The In and Out Spinors
6 Invariance Principles and Conservation Laws
6-a Translational Invariance and Conservation of Momentum
6-b Rotational Invariance and Conservation of Angular Momentum
6-c The Partial-Wave Series for Spinless Particles
6-d Parity
6-e Time Reversal
6-f Invariance Principles for Particles with Spin; Momentum-Space Analysis
6-g Invariance Principles for Particles with Spin; Angular-Momentum Analysis
7 More About Particles with Spin
7-a Polarization and the Density Matrix
7-b The In and Out Density Matrices
7-c Polarization Experiments in (Spin 1/2) — (Spin 0) Scattering
7-d The Helicity Formalism
7-e Some Useful Formulas
8 The Green\'s Operator and the T Operator
8-a The Green\'s Operator
8-b The T Operator
8-c Relation to the Møller Operators
8-d Relation to the Scattering Operator
9 The Born Series
9-a The Born Series
9-b The Born Approximation
9-c The Yukawa Potential
9-d Scattering of Electrons off Atoms
9-e Interpretation of the Born Series in Terms of Feynman Diagrams
10 The Stationary Scattering States
10-a Definition and Properties of the Stationary Scattering States
10-b Equations for the Stationary Scattering Vectors
10-c The Stationary Wave Functions
10-d A Spatial Description of the Scattering Process
11 The Partial-Wave Stationary States
11-a The Partial-Wave S Matrix
11-b The Free Radial Wave Functions
11-c The Partial-Wave Scattering States
11-d The Partial-Wave Lippmann-Schwinger Equation
11-e Properties of the Partial-Wave Amplitude
11-f The Regular Solution
11-g The Variable Phase Method
11-h Iterative Solution for the Regular Wave Function
11-i The Jost Function
11-j The Partial-Wave Born Series
12 Analytic Properties of the Partial-Wave Amplitude
12-a Analytic Functions of a Complex Variable
12-b Analytic Properties of the Regular Solution
12-c Analytic Properties of the Jost Function and S Matrix
12-d Bound States and Poles of the S Matrix
12-e Levinson\'s Theorem
12-f Threshold Behavior and Effective Range Formulas
12-g Zeros of the Jost Function at Threshold
13 Resonances
13-a Resonances and Poles of the S Matrix
13-b Bound States and Resonances
13-c Time Delay
13-d Decay of a Resonant State
14 Additional Topics in Single-Channel Scattering
14-a Coulomb Scattering
14-b Coulomb Plus Short-Range Potentials
14-c The Distorted-Wave Born Approximation
14-d Variational Methods
14-e The K Matrix
15 Dispersion Relations and Complex Angular Momenta
15-a Partial-Wave Dispersion Relations
15-b Forward Dispersion Relations
15-c Nonforward Dispersion Relations
15-d The Mandelstam Representation
I5-e Complex Angular Momenta
15-f Regge Poles
15-g The Watson Transform
16 The Scattering Operator in Multichannel Scattering
16-a Channels
16-b Channel Hamiltonians and Asymptotic States
16-c Orthogonality and Asymptotic Completeness
16-d A Little More Mathematics
16-e The Scattering Operator
17 Cross Sections and Invariance Principles in Multichannel Scattering
17-a The Momentum-Space Basis Vectors
17-b Conservation of Energy and the On-Shell T Matrix
17-c Cross Sections
17-d Rotational Invariance
17-e Time-Reversal Invariance
18 Fundamentals of Time-Independent Multichannel Scattering
18-a The Stationary Scattering States
18-b The Lippman—Schwinger Equations
18-c The T Operators
18-d The Born Approximation; Elastic Scattering
18-e The Born Approximation; Excitation
19 Properties of the Multichannel Stationary Wave Functions
19-a Asymptotic Form of the Stationary Wave Functions; Collisions Without Rearrangement
19-b Asymptotic Form of the Stationary Wave Functions; Rearrangement Collisions
19-c Expansion in Terms of Target States
19-d The Optical Potential
20 Analytic Properties and Multichannel Resonances
20-a Analytic Properties
20-b Proof of Analytic Properties
20-c Bound States
20-d Resonances
20-e Decay of a Multichannel Resonance
21 Two More Topics in Multichannel Scattering
21-a The Distorted-Wave Born Approximation
21-b Final-State Interactions
22 Identical Particles
22-a The Formalism of Identical Particles
22-b Scattering of Two Identical Particles
22-c Multichannel Scattering with Identical Particles
22-d Transition Probabilities and Cross Sections
22-e Electron—Hydrogen Scattering
References
Index