Scattering Theory The Quantum Theory of Nonrelativistic Collisions,9780486450131

Scattering Theory The Quantum Theory of Nonrelativistic Collisions

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ISBN13: 9780486450131
ISBN10: 0486450139
Format: Paperback
Pub. Date: 2006-05-26
Publisher(s): Dover Publications
List Price: $28.57

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Summary

This graduate-level text is intended for any student of physics who requires grounding in the quantum theory of nonrelativistic scattering. The time-dependent approach is emphasized, including the use of time-dependent formalism to define all basic concepts and time-independent theory as a tool for computation. 1983 edition.

Table of Contents

Introduction 1(5)
Mathematical Preliminaries
6(15)
The Hilbert Space of State Vectors
7(2)
Subspaces
9(1)
Operators and Inverses
10(3)
Unitary Operators
13(1)
Isometric Operators
14(2)
Convergence of Vectors
16(3)
Operator Limits
19(2)
The Scattering Operator for a Single Particle
21(17)
Classical Scattering
22(3)
Quantum Scattering
25(3)
The Asymptotic Condition
28(3)
Orthogonality and Asymptotic Completeness
31(3)
The Scattering Operator
34(2)
Unitarity
36(2)
Cross Sections in Terms of the S Matrix
38(18)
Conservation of Energy
39(3)
The On-Shell T Matrix and Scattering Amplitude
42(2)
The Classical Cross Section
44(2)
Definition of the Quantum Cross Section
46(3)
Calculation of the Quantum Cross Section
49(4)
The Optical Theorem
53(3)
Scattering of Two Spinless Particles
56(13)
Two-Particle Wave Functions
57(3)
The Two-Particle S Operator
60(2)
Conservation of Energy-Momentum and the T Matrix
62(2)
Cross Sections in Various Frames
64(2)
The Center-of-Mass Cross Section
66(3)
Scattering of Two Particles with Spin
69(12)
The Hilbert Space for Particles with Spin
70(2)
The S Operator for Particles with Spin
72(1)
The Amplitudes and Amplitude Matrix
73(3)
Sums and Averages Over Spins
76(2)
The In and Out Spinors
78(3)
Invariance Principles and Conservation Laws
81(28)
Translational Invariance and Conservation of Momentum
82(1)
Rotational Invariance and Conservation of Angular Momentum
83(2)
The Partial-Wave Series for Spinless Particles
85(5)
Parity
90(1)
Time Reversal
91(4)
Invariance Principles for Particles with Spin; Momentum-Space Analysis
95(8)
Invariance Principles for Particles with Spin; Angular-Momentum Analysis
103(6)
More About Particles with Spin
109(19)
Polarization and the Density Matrix
109(4)
The In and Out Density Matrices
113(1)
Polarization Experiments in (Spin 1/2) --- (Spin 0) Scattering
114(5)
The Helicity Formalism
119(5)
Some Useful Formulas
124(4)
The Green's Operator and the T Operator
128(15)
The Green's Operator
129(5)
The T Operator
134(1)
Relation to the Moller Operators
135(3)
Relation to the Scattering Operator
138(5)
The Born Series
143(21)
The Born Series
144(3)
The Born Approximation
147(3)
The Yukawa Potential
150(3)
Scattering of Electrons off Atoms
153(4)
Interpretation of the Born Series in Terms of Feynman Diagrams
157(7)
The Stationary Scattering States
164(16)
Definition and Properties of the Stationary Scattering States
165(3)
Equations for the Stationary Scattering Vectors
168(2)
The Stationary Wave Functions
170(3)
A Spatial Description of the Scattering Process
173(7)
The Partial-Wave Stationary States
180(32)
The Partial-Wave S Matrix
181(1)
The Free Radial Wave Functions
182(3)
The Partial-Wave Scattering States
185(3)
The Partial-Wave Lippmann-Schwinger Equation
188(3)
Properties of the Partial-Wave Amplitude
191(6)
The Regular Solution
197(1)
The Variable Phase Method
197(4)
Iterative Solution for the Regular Wave Function
201(3)
The Jost Function
204(3)
The Partial-Wave Born Series
207(5)
Analytic Properties of the Partial-Wave Amplitude
212(26)
Analytic Functions of a Complex Variable
213(2)
Analytic Properties of the Regular Solution
215(2)
Analytic Properties of the Jost Function and S Matrix
217(6)
Bound States and Poles of the S Matrix
223(3)
Levinson's Theorem
226(3)
Threshold Behavior and Effective Range Formulas
229(3)
Zeros of the Jost Function at Threshold
232(6)
Resonances
238(21)
Resonances and Poles of the S Matrix
240(5)
Bound States and Resonances
245(4)
Time Delay
249(4)
Decay of a Resonant State
253(6)
Additional Topics in Single-Channel Scattering
259(26)
Coulomb Scattering
259(7)
Coulomb Plus Short-Range Potentials
266(4)
The Distorted-Wave Born Approximation
270(3)
Variational Methods
273(7)
The K Matrix
280(5)
Dispersion Relations and Complex Angular Momenta
285(30)
Partial-Wave Dispersion Relations
287(4)
Forward Dispersion Relations
291(3)
Nonforward Dispersion Relations
294(3)
The Mandelstam Representation
297(5)
Complex Angular Momenta
302(4)
Regge Poles
306(2)
The Watson Transform
308(7)
The Scattering Operator in Multichannel Scattering
315(23)
Channels
316(5)
Channel Hamiltonians and Asymptotic States
321(5)
Orthogonality and Asymptotic Completeness
326(5)
A Little More Mathematics
331(3)
The Scattering Operator
334(4)
Cross Sections and Invariance Principles in Multichannel Scattering
338(20)
The Momentum-Space Basis Vectors
339(3)
Conservation of Energy and the On-Shell T Matrix
342(4)
Cross Sections
346(5)
Rotational Invariance
351(2)
Time-Reversal Invariance
353(5)
Fundamentals of Time-Independent Multichannel Scattering
358(14)
The Stationary Scattering States
359(2)
The Lippmann-Schwinger Equations
361(2)
The T Operators
363(1)
The Born Approximation; Elastic Scattering
364(3)
The Born Approximation; Excitation
367(5)
Properties of the Multichannel Stationary Wave Functions
372(19)
Asymptotic Form of the Stationary Wave Functions; Collisions Without Rearrangement
373(5)
Asymptotic Form of the Stationary Wave Functions; Rearrangement Collisions
378(2)
Expansion in Terms of Target States
380(3)
The Optical Potential
383(8)
Analytic Properties and Multichannel Resonances
391(27)
Analytic Properties
392(4)
Proof of Analytic Properties
396(9)
Bound States
405(2)
Resonances
407(6)
Decay of a Multichannel Resonance
413(5)
Two More Topics in Multichannel Scattering
418(16)
The Distorted-Wave Born Approximation
418(6)
Final-State Interactions
424(10)
Identical Particles
434(29)
The Formalism of Identical Particles
435(6)
Scattering of Two Identical Particles
441(7)
Multichannel Scattering with Identical Particles
448(2)
Transition Probabilities and Cross Sections
450(4)
Electron-Hydrogen Scattering
454(9)
References 463(4)
Index 467

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