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| Gudder S.P. — Stochastic methods in quantum mechanics |
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| Предметный указатель |
 -algebra 10
-class 68 69
-convex structure 77
-isomorphism 20
-orthocompleteness 42
Absolute continuity 29 37
action 169
Action, quasi-invariant 169
Additivity 72
Adjoint 116
Affine functionals 77
Algebra, Banach 132
Algebra, C* 131 132
Algebra, normed 132
Algebraic approach 137
Annihilation operator 192
Antilattice 57
Approximate observable position 105
atom 3 60
Atom, hydrogen 5
atomic 60 102 129
Averaging property 90
Beam 76 81
Beam, strength 76 80
Birkhoff, G. 35
Bohr postulates 4 5
Bohr, N. 3 4
Boltzmann’s constant 1
Boolean -algebra 47 48
Boolean -algebra, separable 49
Borchers, H. 199
Borel sets 10
Borel — Cantelli theorem 23
Born, M. 6 7
Boson 190
Boson, subspace 190
Brown, R. 142
Canonical commutation relations (CCR) 166 198
Canonical commutation relations (CCR), Heisenberg form 166
Canonical commutation relations (CCR), Schrodinger form 166
Canonical commutation relations (CCR), Weyl form 166 174
Canonical pair 24
Canonical pair, identically distributed 26
Canonical pair, independent 26
Cantelli’s lemma 23
Cantoni, V. 36 38
Center 60
Central limit theorem 24 27
Characteristic function 147
Characteristic function, joint 148
Chebyshev’s inequality 51
Classical mechanics 2 3 8
Cluster property 184
Commutation relation 9 24
Compatant 48
Compatibility 44 45 48
Compatible completeness 60
Complementation 11 40
Complete separability 171
Compton effect 3 5
Condition C 49
Condition E 55 57 71
Condition U 55
Conditional expectation 28 29 30 32 88 89 91
Conditional probability 28 29 85 94
Cone 95 100
Cone, backward 179
Cone, forward 179
containment 11
Convergence, almost everywhere 24
Convergence, almost uniform 24
Convergence, in distribution 26 27
Convergence, in probability 24
Convergence, weak 26
Convex combinations 75
Convex structure 76
Convex structure, total 94
Correlation function 160
Coulomb, force 4
Coulomb, potential 5
Course-graining 33
Covariance matrix 26 155
Creation operator 192
Cushen — Hudson theorem 24 27
Cyclic vector 134 138 175
Cycon, H. 90 109
Davies, E. 75 86 87 101 102 105 106 108
Davisson — Germer experiment 5
De Broglie waves 5 6 7
de Broglie, L. 5
Delta function 114
Detection screen 14 17
Diffraction pattern 16 17
Dirac, P. 5 7 12
Dispersion-free state 60
distribution 10 12 51
Distribution, finite-dimensional 93
Distribution, joint 10 18 83 85
Distribution, normal 27
Distribution, operator 25
Dominated Convergence Theorem 24
Double-slit experiment 14 33
Duality principle 5
Edwards, C 108
Effect 77 78
Effectiveness 91
Egorov’s theorem 24
Eigenvalue 5 6 7
Einstein, A. 3 142
electric field 5
Electromagnetic waves 2 4 5
Electromagnetic waves, hydrogen 4 7 8 9
Electron 3 4 5 6
Electron, orbit 4
Energy 1 2 3 4 6
Energy, kinetic 3 4 8
Energy, observable 8
Energy, potential 4 8
Energy-momentum operator 182
entropy 33
Equipartition principle 1
Euclidean group 194
Evenness 121
Event 39 41 42
Event, complement 40
Event, quantum 11
Event, structure 42
Event, structure, coherent 60
Event, structure, convex 52
Event, structure, trivial 60
Expectation (mean) 9 10 51 90
Extension Principle 116 119 120
Fatou’s Lemma 24
Fermion 190
Field operator 181 199
Foch space 189 191 199
Foch space, boson 191
Fourier transform 119
Fourier transform, inverse 119
Frechet space 111 112
frequency 1 2 3 4 6
Functionals, affine 77
Functionals, characteristic 147
Functionals, correlation 147
Functionals, covariance 147
Functionals, mean 147
Functionals, variance 147
Gelfand — Naimark — Segal (GNS) construction 32 134
Gelfand, I. 162 174
Gibbs probability 2
| Gleason, A. 129 139
Greatest lower bound (inf) 40
Heisenberg 5
Hellwig, K. 90 109
Hemi-continuity 121
Hidden variables 59
Hidden variables, in von Neumann sense 60 61
Hidden variables, theory 62
Hidden variables, theory, minimal 62
Hyperplane 95
Increments, independent 142
Increments, stationary 142
Independent values 162
Indexed stochastic process 141
Instrument 81 82
Instrument, composition 83 107 108
Instrument, dual 89
Instrument, nuclear 92
Interference 6 16
Interference, probability 14 33
Interference, quantum 14
Intersection 11
Intrinsic metric 97
Involution 131
Isomorphic convex structures 77
Isomorphic linear spaces 95
Isomorphic measure spaces 154
Jauch, J. 35
Kolmogorov, M. 6 10
L-additivity 130
L-orthogonality 130
Laplacian 5
Lattice 44 47
Lattice, distributive 47
Law of Large Numbers 24
Least upper bound (sup) 40
Lewis, J. 75 101 102 108
Light energy 4
Light spectrum 3
Limit theorems 21
Locality 181 182 183 186
Lorentz group 180
Lorentz group, inhomogeneous 180
Louton, T. 51 52 72
Ludwig, G. 75 108
Mackey, G. 35 72
Maczynski 72
Mean value property 90
Mean vector 149
Measure 10
Measure, positive-operator-valued (POV) 86 105
Measure, probability 10 21 42
Measure, projection-valued (PV) 86 105
Measure, space 10
Measurement 36
Measurement, simultaneous 18
Mielnik, B. 75 108
Minkowski space 179
Mixtures 75
Moments 26
Momentum 5 6
Momentum, observable 8 9
Monotonically weak*-continuity 90
Morgenstern, O. 75
Nelson, E. 18 193 196 197 198 199
Nonnegativity 121
Normalization 97
Nuclear theorem 120
Nucleus 3
Number of particles operator 191
Observability 7 8 11 36 39 44 45 79 84
Observability, bounded 55
Observability, commuting 17 18
Observability, independent 33
Observability, measurable 30
Observability, sum 55
Oddness 121
Operation 81
Operator, correlation 149
Operator, covariance 149
Operator, density 12 85
Operator, projection 11
Operator, self-adjoint 7 18
Operator, trace-class 12
Order determination 42
Orthocomplement 42
Orthogonal additivity 121
Orthogonal increase 124
Partially ordered set (poset) 40 42
Partially ordered set (poset), orthocomplemented 41 42
Partially ordered set (poset), orthomodular 42
Pauli symmetrization principle 190
Phase space 47
photoelectric effect 3 5
Photon 5
Piron, C. 35 139
Planck, M. 1 2 3
Planck’s postulate 4
Planck’s radiation law 2 3
Poincare group 180
Polynomial bounded function 113 117 119
Position (coordinate) 5 6
Position (coordinate), observable 8 9
Positive definite function 148
Positive linear functional 131
Positive linear functional, dominating 169
Preparation 36
Probability, classical 6 10 11 12 84
Probability, quantum 8 11
Probability, space 10
Probability, space, generalized 68
Probability, transition 17 36 38 94
Prohorov, Y. 153
Proposition 41 78 86
Quantum of energy 1 2 6
Quantum, logic 42 45 69
Quantum, orbits 3
Radiation, electromagnetic 5
Radiation, heat 1
Radiation, light 4
Radon — Nikodym theorem 29
Ramsey, A. 49 72
Random field 145 146 163
Random field, covariant 169 171 194
Random field, derivative of 160
Random field, ergodic 194
Random field, Euclidean 194 198 199
Random field, full 158
Random field, Gaussian 150 163
Random field, generated 145 153 160
Random field, isonormal 150 151
Random field, Markov 163 194
Random field, proper 148 150
Random field, regular 197
Random field, T-covariant 169
Random field, unit Gaussian 145 198
Random functional 145
Random functional, bounded 147
Random functional, continuous 145
Random functional, equivalent 145
Random functional, linear 145
Random functional, second order 147
Random functional, uncorrelated 147 150
Random variables 10
Random variables, corresponding 154
Random variables, full set of 157
Random variables, Gaussian 154
Random variables, independent 11 22 23 84
Random variables, jointly Gaussian 154
Rao, M. 131
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