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Beltrametti E.G., Cassinelli G. Ч The Logic of Quantum Mechanics (Encyclopedia of Mathematics and Its Applications - Vol 15)
Beltrametti E.G., Cassinelli G. Ч The Logic of Quantum Mechanics (Encyclopedia of Mathematics and Its Applications - Vol 15)



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Ќазвание: The Logic of Quantum Mechanics (Encyclopedia of Mathematics and Its Applications - Vol 15)

јвторы: Beltrametti E.G., Cassinelli G.

јннотаци€:

This volume deals with the foundations as well as the fascinating logic of quantum mechanics. The thorough presentation will guide the reader to a unified view of a theory that together with relativity is regarded as the greatest achievement in physics during this century.


язык: en

–убрика: ћатематика/

—татус предметного указател€: √отов указатель с номерами страниц

ed2k: ed2k stats

»здание: 1 edition

√од издани€: 1981

 оличество страниц: 305

ƒобавлена в каталог: 12.04.2010

ќперации: ѕоложить на полку | —копировать ссылку дл€ форума | —копировать ID
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ѕредметный указатель
$\mathcal{P}(\mathcal{K})$      105Ч108
Atom of a lattice      98
Baer*-semigroups      178
Baer*-semigroups and orthomodular lattices      177Ч179
Baer*-semigroups, closed projections of      178
BellТs inequality      275
Boolean algebra      97
Boolean algebra, partied      267
Boolean algebra, sub algebra of poset      126
Borel sets      4
Center of lattice      128
Certainly-yes domain      142Ч143
Chain in a lattice      195
Chain in a lattice, f-closed subspaces      233
Closure relation      120 193 201
Closure relation, orthoclosure      202 212
Closure spaces      193
Closure spaces, closed subspaces of      193
Coherent subspaces      48Ч49
Commutativity in poset      125Ч128
Commuting self-adjoint operators      19
Complementarity      26 162Ч164
Composition conditions      258
Composition of physical systems      61Ч74 256Ч264
Conditional connective      222
Conditional connective, classical      222
Conditional connective, MittelstaedtТs.      224
Conditional connective, quantum      222Ч225
Conditioned probability with respect to Boolean algebra      285Ч287
Conditioned probability with respect to event      279Ч283
Conjunction      219Ч220
Continuous geometry      110
Convex set of states      6 209
Convex set of states, normed functioned on.      209
Convex set of states, polytope      211
Convex set of states, simplex      213
Convex set of states, strong polytope      213
Coordinatization, Hilbert-space      235Ч237
Coordinatization, vector-space      230Ч234
Coproduct of lattices      259
Correlation between subsystems      67Ч 72 81
Correlation between subsystems, coefficient of      68 273
Covering property      98 123 133 230
Cyclic vector      294
de MorganТs laws      96 221
Density operators      4
Direct product of lattices      131
Direct sum of lattices      131
Disjoint elements      97
Disjunction      220
Distributive triple      97
Dynamical group      53
Dynamical invariance      244
Dynamics      52Ч58 249Ч255
Dynamics of subsystems      72Ч73
Dynamics, Heisenberg picture      56Ч57 254
Dynamics, Markovian      54 250
Dynamics, reversible      54 251
Dynamics, Schroedinger equation      55Ч56
Dynamics, Schroedinger picture      53
Dynamics, stationary      54 250
Einstein, Podolsky, Rosen paradox      69Ч 72
Entropy of a state      287
Euclidean invariance      41Ч43
Evolution operator      53
Exclusion principle      65
Faces of convex set      210
Faces of convex set, detectable      211
Faces of convex set, orthoclosed      212
Faces of convex set, stable      213
FLATS      195Ч197
Free particle      37Ч41
Free particle, $G_{12}$      101
GleasonТs theorem      115
GreechieТs examples      102
Hamiltonian of free particle      39 247
Hamiltonian operator      55Ч56 252Ч254
Heisenberg inequalities      24Ч26
Hermitian form      233
Hidden-variable theories      171 265
Hidden-variable theories, BellТs inequality      275
Hidden-variable theories, BellТs model of      268Ч270
Hidden-variable theories, contextual      172Ч174 175Ч176 271-276
Hidden-variable theories, Kochen and Specker model of      270Ч271
Hidden-variable theories, local      271Ч276
Hidden-variable theories, noncontextual      172Ч175 265Ч 271
Identical systems      63Ч65
Imprimitivity system      244
Induced representations      244
Information of state      287
Involution of field      233
Involutive ring      102
Involutive ring, projections of      103
Involutive semigroup      178
Involutive semigroup, projections of      178
Irreducibility      128 134
Isomorphism of orthomodular lattices      130
Join      96
Joint distributions      23 158
Lattices      97
Lattices, A. C.      95
Lattices, amalgamation      102
Lattices, atomic      98
Lattices, atomistic      98
Lattices, complete      97
Lattices, distributive      97
Lattices, implicative      224
Lattices, irreducible      128
Lattices, modular      98
Lattices, orthomodular      97
Lattices, separable      97
Logic of physical system      149 152
Measurement      79 181
Measurement ideal and of first kind      79 180Ч187
Measurement process      77Ч86
Measuring instrument      77Ч86
Meet      96
Mixtures      7 139
Mixtures, decomposition into pure states      7Ч12
Mixtures, ignorance interpretation of      11Ч12
Mixtures, nonunique decomposability      9Ч12 34Ч37
Modular geometric lattices      232
Modularity      98 107
Modus ponendo ponens      223
Momentum of free particle      38
Morphism of orthomodular lattices      130
Negation      220Ч221
Nonseparability      71
Observables      153
Observables, associated with $\mathcal{P}(\mathcal{K})$      155
Observables, bounded      153
Observables, compatible      155
Observables, complementarity      162Ч164
Observables, complete set of compatible      157
Observables, function of      156Ч157
Observables, joint distribution of compatible      158
Observables, mean value      154
Observables, spectrum      153 158
Observables, sum of      159Ч161
Observables, variable      154
Operators commuting self-adjoint      19
Operators commuting self-adjoint, complete set of commuting self-adjoint      21
Operators commuting self-adjoint, density      4
Operators commuting self-adjoint, positive      291
Operators commuting self-adjoint, spectral representation      293
Operators commuting self-adjoint, spectrum      14
Operators commuting self-adjoint, trace-class      291Ч292
Order relation      96
Orthocomplement      96
Orthocomplementation      96 144
Orthocomplementation, relative      130
Orthomodularity      97 229Ч230
Paradoxes E. P. R.      69Ч72
Paradoxes E. P. R., Schroedinger cat      84Ч86
Pauli matrices      31
Physical quantities compatible      19
Physical quantities compatible, as proposition-valued measures      150
Physical quantities compatible, complementary      26
Physical quantities compatible, complete set of compatible      21
Physical quantities compatible, function of compatible      19
Physical quantities compatible, joint probability distributions      23
Physical quantities compatible, mean value      16
Physical quantities compatible, probability distribution      4Ч5
Physical quantities compatible, probability distribution in a pure state      8
Physical quantities compatible, variance      17
Polytope      211
Polytope, strong      213
POSET      96
Poset, orthocomplete      97
Poset, orthomodular      97
Position of free particle      38
Probability measures      111
Probability measures and covering property      123Ч124
Probability measures, convex combination of      112
Probability measures, dispersion-free      155
Probability measures, on $9(0C)$      115 117 118 121 122
Probability measures, on $G_{12}$      114 116 118 121 122
Probability measures, ordering set of      116
Probability measures, pure      112 122Ч123
Probability measures, separating set of      116
Probability measures, strongly ordering set of      116
Probability measures, sufficient set of      116
Probability measures, superposition of      120
Probability measures, support of      117
Probability space      172 277
Probability space, generalized      278
Projection postulate von NeumannТs      79
Projection postulate von NeumannТs, LuedersТs      79 182 282Ч283
Projection-valued measures      294
Projection-valued measures, spectral      4
Projective geometry      232
Projective lattice      232
Proposition-valued measures      150
Propositions      140Ч142 146Ч149
Propositions, active picture of      187Ч188
Propositions, compatible      155Ч156
Propositions, complementary      162Ч164
Propositions, lattice of      152Ч153
Propositions, ordering      142Ч144
Propositions, orthocomplements      144Ч146
Propositions, orthogonal      148
Propositions, passive picture of      187Ч188
Quantum logic      217Ч225
Quantum superpositions      164Ч167
Quantum superpositions, exchange property of      167
Random variables      155 277Ч278
Rank      194Ч196
Recognition maps      257
Residuated mappings      179
Sasaki projections      99 179
Sasaki projections, properties of      180Ч181
Schroedinger equation      55Ч56
Segment of lattice      130
Spectral theorem      293 295
Spectrum continuous      15 158
Spectrum continuous of observables      153
Spectrum continuous of self-adjoint operators      14
Spectrum continuous, point      14 158
Spectrum continuous, simple      294
Spin      30Ч31
Spin, spin-$\frac{1}{2}$ system      31Ч34
Spin-statistics connection      65
States of compound systems      65Ч67
States of subsystems      65Ч67 (see also УProbability measuresФ)
States, dispersion-free      155 (see also УProbability measuresФ)
States, exceptional      268Ч271 (see also УProbability measuresФ)
States, mixture      7 (see also УProbability measuresФ)
States, nonpure      7 139
States, pure      7 140
States, superposition of      8 120 164Ч167 191Ч193
States, vector      8 (see also УProbability measuresФ)
StoneТs theorem      55 245 253
Superposition principle      165
Superselection operators      47
Superselection rules      45Ч51 167 238Ч239
Superselection rules and compound systems      73
Superselection rules, continuous      48
Superselection rules, discrete      48
Support      117 299
Tensor product      61 263Ч264
Tensor product, antisymmetrical      64
Tensor product, symmetrical      64
Trace-class operators      291Ч292
Transition probability      12 200
Transition-probability spaces      200
Transition-probability spaces, basis of      202
Transition-probability spaces, orthoclosed subsets of      202
Transition-probability spaces, subspaces of      201
Two-slit experiment      283Ч285
Von Neumann algebras      21 109Ч110
von Neumann algebras, entropy      287
von Neumann algebras, lattices      110
von Neumann algebras, projection postulate      79
Weights      6 112
WignerТs theorem      253
Yes-no experiments      137Ч138 208Ч210
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