Density Matrix Theory and Applications

Couverture
Springer Science & Business Media, 31 oct. 1996 - 327 pages
Quantum mechanics has been mostly concerned with those states of systems that are represented by state vectors. In many cases, however, the system of interest is incompletely determined; for example, it may have no more than a certain probability of being in the precisely defined dynamical state characterized by a state vector. Because of this incomplete knowledge, a need for statistical averaging arises in the same sense as in classical physics. The density matrix was introduced by J. von Neumann in 1927 to describe statistical concepts in quantum mechanics. The main virtue of the density matrix is its analytical power in the construction of general formulas and in the proof of general theorems. The evaluation of averages and probabilities of the physical quantities characterizing a given system is extremely cumbersome without the use of density matrix techniques. The representation of quantum mechanical states by density matrices enables the maximum information available on the system to be expressed in a compact manner and hence avoids the introduction of unnecessary variables. The use of density matrix methods also has the advan tage of providing a uniform treatment of all quantum mechanical states, whether they are completely or incompletely known. Until recently the use of the density matrix method has been mainly restricted to statistical physics. In recent years, however, the application of the density matrix has been gaining more and more importance in many other fields of physics.
 

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Table des matières

Basic Concepts
1
112 The Polarization Vector
4
113 Mixed Spin States
8
114 Pure versus Mixed States
10
115 The SpinDensity Matrix and Its Basic Properties
12
116 The Algebra of the Fault Matrices
19
117 Summary
22
122 Pure and Mixed Polarization States of Photons
25
542 Quantum Beats Produced by Symmetry Breaking
154
55 Time Integration over Quantum Beats
156
552 Depolarization Effects Caused by Fine and Hyperfine Interactions
158
Some Applications
161
612 Influence of Fine and Hyperfine Interactions on the Emitted Radiation
166
62 SteadyState Excitation
167
622 Threshold and Pseudothreshold Excitations
170
63 Effect of a Weak Magnetic Field
172

123 The Quantum Mechanical Concept of Photon Spin
27
124 The Polarization Density Matrix
29
125 Stokes Parameter Description
32
General Density Matrix Theory
39
22 The Density Matrix and Its Basic Properties
43
23 Coherence versus Incoherence
47
232 The Concept of Coherent Superposition
49
24 Time Evolution of Statistical Mixtures
52
242 The Liouville Equation
55
243 The Interaction Picture
57
25 Spin Precession in a Magnetic Field
62
26 Systems in Thermal Equilibrium
63
Coupled Systems
67
32 Interaction with an Unobserved System The Reduced Density Matrix
69
33 Analysis of Light Emitted by Atoms Nuclei
73
332 Description of the Emitted Photon
76
34 Some Further Consequences of the Principle of Nonseparability
77
342 Complete Coherence in Atomic Excitation
79
35 Excitation of Atoms by Electron Impact I
81
352 Restrictions due to Symmetry Requirements
86
4 Irreducible Components of the Density Matrix
91
42 The Definition of Tensor Operators
92
422 Transformation Properties under Rotations The Rotation Matrix
94
423 Examples
97
424 Some Important Properties of the Tensor Operators
99
43 State Multipoles Statistical Tensors
101
432 Basic Properties of State Multipoles
103
433 Physical Interpretation of State Multipoles The Orientation Vector and Alignment Tensor
104
Spin Tensors
106
442 Description of Spin1 Particles
107
45 Symmetry Properties Relation between Symmetry and Coherence
111
452 Classification of Axially Symmetric Systems
112
Photoabsorption by Atoms Nuclei
117
462 General Consequences of Reflection Invariance
120
463 Axially Symmetric Atomic Systems
122
464 Symmetry Relations in the Natural System
123
465 Coordinate Representation of the Density Matrix Shape and Spatial Orientation of Atomic Charge Clouds
125
47 Time Evolution of State Multipoles in the Presence of an External Perturbation
131
472 Perturbation Coefficients for the Fine and Hyperfine Interactions
133
473 An Explicit Example
138
474 Influence of an External Magnetic Field
139
48 Notations Used b Other Authors
141
Radiation from Polarized Atoms Quantum Beats
143
Separation of Dynamical and Geometrical Factors
147
53 Discussion of the General Formulas
149
532 Manifestations of Coherence Quantum Beats
151
54 Perturbed Angular Distribution and Polarization
153
632 Magnetic Depolarization Theory of the Hanle Effect
175
633 Physical Interpretation of Zeeman Quantum Beats Rotation of the Atomic Charge Cloud
180
64 Influence of Electric Fields OrientationAlignment Conversion
182
642 Variation of Shape and Spatial Direction of Atomic Charge Clouds
184
643 Creation of Orientation out of Alignment
187
The Role of Orientation and Alignment in Molecular Processes
189
Distribution Functions of Angular Momentum Vectors
190
73 Axis Distributions of Linear Rotors
195
732 General Equations Examples and Experimental Studies
196
General Description of Axis Orientation and Alignment
200
742 Relation between Angular Momenta and Axis Distributions for Linear Rotors Pendulum States
204
75 Angular Momenta and Axis Distributions of Rotors after Photoabsorption Quantum Mechanical and Classical Theory
206
752 Absorption of Circularly Polarized and Unpolarized Light
209
76 Distribution Functions for Nonlinear Molecules and for Diatomics with Electronic Angular Momentum
212
762 Angular Momentum and Axis Distributions of Symmetric Tops
213
763 Theory of Oriented SymmetricTop Molecules Semiclassical Interpretation
216
764 Order Parameters for Nonlinear Molecules
218
77 Electronic Orbital Orientation and Alignment
220
Spatial Orientation and Selective Population
225
773 Combined Description of Rotational Polarization and Orbital Anisotropies
229
774 Vector Correlations Analysis of Emitted Light
233
775 Photoabsorption and Photofragmentation
238
78 Dynamical Stereochemistry
241
782 Discussion and Examples
248
783 Product Rotational Polarization Quantum Mechanical Theory and Semiclassical Approximation
253
784 AlignmentInduced Chemical Reactions
257
Quantum Theory of Relaxation
261
812 Time Correlation Functions Discussion of the Markoff Approximation
264
813 The Relaxation Equation The Secular Approximation
267
82 Rate Master Equations
270
83 Kinetics of Stimulated Emission and Absorption
275
84 The Bloch Equations
282
842 Longitudinal and Transverse Relaxation Spin Echoes
286
843 The Optical Bloch Equations
290
85 Some Properties of the Relaxation Matrix
291
852 Relaxation of State Multipoles
293
86 The Liouville Formalism
295
87 Linear Response of a Quantum System to an External Perturbation
299
Appendixes
303
State Multipoles for Coupled Systems
306
Formulas from Angular Momentum Theory
308
The Efficiency of a Measuring Device
312
The Scattering and Transition Operators
314
References
317
Index
321
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