Contextual approach to quantum formalism:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin
Springer
2009
|
| Schriftenreihe: | Fundamental Theories of Physics
160 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XXVIII, 353 S. 235 mm x 155 mm |
| ISBN: | 9781402095924 ebooks 9781402095931 |
Internformat
MARC
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| 016 | 7 | |a 991181956 |2 DE-101 | |
| 020 | |a 9781402095924 |c Gb. : ca. EUR 117.65 (freier Pr.), ca. sfr 182.50 (freier Pr.) |9 978-1-4020-9592-4 | ||
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| 084 | |a UK 1200 |0 (DE-625)145792: |2 rvk | ||
| 084 | |a 520 |2 sdnb | ||
| 100 | 1 | |a Khrennikov, Andrei |d 1958- |e Verfasser |0 (DE-588)128568410 |4 aut | |
| 245 | 1 | 0 | |a Contextual approach to quantum formalism |c Andrei Khrennikov |
| 264 | 1 | |a Berlin |b Springer |c 2009 | |
| 300 | |a XXVIII, 353 S. |c 235 mm x 155 mm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Fundamental Theories of Physics |v 160 | |
| 650 | 4 | |a Quantentheorie | |
| 650 | 4 | |a Quantum theory | |
| 650 | 0 | 7 | |a Wahrscheinlichkeitstheorie |0 (DE-588)4079013-7 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Quantenmechanik |0 (DE-588)4047989-4 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Quantenmechanik |0 (DE-588)4047989-4 |D s |
| 689 | 0 | 1 | |a Wahrscheinlichkeitstheorie |0 (DE-588)4079013-7 |D s |
| 689 | 0 | |5 DE-604 | |
| 830 | 0 | |a Fundamental Theories of Physics |v 160 |w (DE-604)BV000012461 |9 160 | |
| 856 | 4 | 2 | |m SWB Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017629583&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-017629583 | ||
Datensatz im Suchindex
| _version_ | 1804139228968255488 |
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| adam_text | CONTENTS PREFACE .................................. . . . . . . . . . .
. . . . . . . . . . . . . . . . VII ACKNOWLEDGEMENTS . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . XVII PART I QUANTUM AND CLASSICAL PROBABILITY 1 QUANTUM MECHANICS:
POSTULATES AND INTERPRETATIONS . . . . . . . . . . . . . . . 3 1.1
QUANTUM MECHANICS . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . 3 1.1.1 MATHEMATICAL BASIS . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . 3 1.1.2 POSTULATES . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . 5 1.2 PROJECTION POSTULATE, COLLAPSE OF WAVE FUNCTION,
SCHROEDINGER*S CAT 11 1.2.1 VON NEUMANN*S PROJECTION POSTULATE . . . . .
. . . . . . . . . . . . . . . 12 1.2.2 COLLAPSE OF WAVE FUNCTION . . . .
. . . . . . . . . . . . . . . . . . . . . . . . 12 1.2.3 SCHROEDINGER*S
CAT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . 13 1.2.4 LUEDERS PROJECTION POSTULATE . . . . . . . . . . . . . . . .
. . . . . . . . . . . . 14 1.3 STATISTICAL MIXTURES . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 1.4 VON
NEUMANN*S AND LUEDERS* POSTULATES FOR MIXED STATES. . . . . . . . . . 17
1.5 CONDITIONAL PROBABILITY . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . 21 1.6 DERIVATION OF INTERFERENCE OF
PROBABILITIES . . . . . . . . . . . . . . . . . . . . . . 23 XXI XXII
CONTENTS 2 CLASSICAL PROBABILITY THEORIES . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . 27 2.1 KOLMOGOROV
MEASURE-THEORETIC MODEL . . . . . . . . . . . . . . . . . . . . . . . .
28 2.1.1 FORMALISM . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . 28 2.1.2 DISCUSSION . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 2.2 VON
MISES FREQUENCY MODEL . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . 33 2.2.1 COLLECTIVE (RANDOM SEQUENCE) . . . . . . . . .
. . . . . . . . . . . . . . . . 33 2.2.2 DIFFICULTIES WITH DEFINITION OF
RANDOMNESS. . . . . . . . . . . . . . . 34 2.2.3 S -SEQUENCES . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
2.2.4 OPERATIONS FOR COLLECTIVES . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . 36 2.3 COMBINING AND INDEPENDENCE OF COLLECTIVES . . .
. . . . . . . . . . . . . . . . . 41 PART II CONTEXTUAL PROBABILITY AND
QUANTUM-LIKE MODELS 3 CONTEXTUAL PROBABILITY AND INTERFERENCE . . . . .
. . . . . . . . . . . . . . . . . . . . . 47 3.1 VAEXJOE MODEL: CONTEXTUAL
PROBABILITY . . . . . . . . . . . . . . . . . . . . . . . . . . 49 3.1.1
CONTEXTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . 49 3.1.2 OBSERVABLES . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . 49 3.1.3
CONTEXTUAL PROBABILITY SPACE AND MODEL . . . . . . . . . . . . . . . . .
50 3.1.4 VAEXJOE MODELS INDUCED BY THE KOLMOGOROV MODEL . . . . . . . . .
53 3.1.5 VAEXJOE MODELS INDUCED BY THE QUANTUM MODEL . . . . . . . . . . .
55 3.1.6 VAEXJOE MODELS INDUCED BY THE VON MISES MODEL . . . . . . . . . .
. 56 3.2 CONTEXTUAL PROBABILISTIC DESCRIPTION OF DOUBLE SLIT EXPERIMENT
. . . . 57 3.3 FORMULA OF TOTAL PROBABILITY AND MEASURES OF
SUPPLEMENTARITY . . . . 59 3.4 SUPPLEMENTARY OBSERVABLES . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . 62 3.5 PRINCIPLE OF
SUPPLEMENTARITY . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . 63 3.6 SUPPLEMENTARITY AND KOLMOGOROVNESS . . . . . . . . . .
. . . . . . . . . . . . . . . 64 3.6.1 DOUBLE STOCHASTICITY AS THE LAW
OF PROBABILISTIC BALANCE . . . 66 3.6.2 PROBABILISTICALLY BALANCED
OBSERVABLES . . . . . . . . . . . . . . . . . . 66 3.6.3 SYMMETRICALLY
CONDITIONED OBSERVABLES . . . . . . . . . . . . . . . . . 69 CONTENTS
XXIII 3.7 INCOMPATIBILITY, SUPPLEMENTARITY AND EXISTENCE OF JOINT
PROBABILITY DISTRIBUTION . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . 70 3.7.1 JOINT PROBABILITY DISTRIBUTION . . .
. . . . . . . . . . . . . . . . . . . . . . . 71 3.7.2 COMPATIBILITY AND
PROBABILISTIC COMPATIBILITY . . . . . . . . . . . . 72 3.8
INTERPRETATIONAL QUESTIONS . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . 74 3.8.1 CONTEXTUALITY . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . 74 3.8.2 REALISM .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . 75 3.9 HISTORICAL REMARK: COMPARING WITH MACKEY*S MODEL .
. . . . . . . . . . . 76 3.10 SUBJECTIVE AND CONTEXTUAL PROBABILITIES IN
QUANTUM THEORY . . . . . . . 78 4 QUANTUM-LIKE REPRESENTATION OF
CONTEXTUAL PROBABILISTIC MODEL . . . 81 4.1 TRIGONOMETRIC, HYPERBOLIC,
AND HYPER TRIGONOMETRIC CONTEXTS . . . . 82 4.2 QUANTUM-LIKE
REPRESENTATION ALGORITHM*QLRA . . . . . . . . . . . . . . . 84 4.2.1
PROBABILISTIC DATA ABOUT CONTEXT . . . . . . . . . . . . . . . . . . . .
. . . 84 4.2.2 CONSTRUCTION OF COMPLEX PROBABILISTIC AMPLITUDES . . . .
. . . . 85 4.3 HILBERT SPACE REPRESENTATION OF B -OBSERVABLE . . . . . .
. . . . . . . . . . . . 88 4.3.1 BORN*S RULE . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . 88 4.3.2
FUNDAMENTAL PHYSICAL OBSERVABLE: VIEWS OF DE BROGLIE AND BOHM . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. 89 4.3.3 B -OBSERVABLE AS MULTIPLICATION OPERATOR . . . . . . . . . .
. . . . . . . 89 4.3.4 INTERFERENCE . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . 90 4.4 HILBERT SPACE
REPRESENTATION OF A -OBSERVABLE . . . . . . . . . . . . . . . . . . 91
4.4.1 CONVENTIONAL QUANTUM AND QUANTUM-LIKE REPRESENTATIONS . 91 4.4.2 A
-BASIS FROM INTERFERENCE . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . 92 4.4.3 NECESSARY AND SUFFICIENT CONDITIONS FOR BORN*S RULE.
. . . . . . 93 4.4.4 CHOICE OF PROBABILISTIC PHASES . . . . . . . . . .
. . . . . . . . . . . . . . . 95 4.4.5 CONTEXTUAL DEPENDENCE OF A
-BASIS. . . . . . . . . . . . . . . . . . . . . . 96 XXIV CONTENTS 4.4.6
EXISTENCE OF QUANTUM-LIKE REPRESENTATION WITH BORN*S RULE FOR BOTH
REFERENCE OBSERVABLES . . . . . . . . . . . . . . . . . . . 97 4.4.7
*PATHOLOGIES* . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . 99 4.5 PROPERTIES OF MAPPING OF TRIGONOMETRIC
CONTEXTS INTO COMPLEX AMPLITUDES . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 4.5.1
CLASSICAL-LIKE CONTEXTS . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . 100 4.5.2 NON-INJECTIVITY OF REPRESENTATION MAP . . . . .
. . . . . . . . . . . . . 101 4.6 NON-DOUBLE STOCHASTIC MATRIX:
QUANTUM-LIKE REPRESENTATIONS . . . . 101 4.7 NONCOMMUTATIVITY OF
OPERATORS REPRESENTING OBSERVABLES . . . . . . . . 104 4.8 SYMMETRICALLY
CONDITIONED OBSERVABLES . . . . . . . . . . . . . . . . . . . . . . .
105 4.8.1 B -SELECTIONS ARE TRIGONOMETRIC CONTEXTS . . . . . . . . . . .
. . . . . . 106 4.8.2 EXTENSION OF REPRESENTATION MAP . . . . . . . . .
. . . . . . . . . . . . . . 109 4.9 FORMALIZATION OF THE NOTION OF
QUANTUM-LIKE REPRESENTATION . . . . . 109 4.10 DOMAIN OF APPLICATION OF
QUANTUM-LIKE REPRESENTATION ALGORITHM 113 5 ENSEMBLE REPRESENTATION OF
CONTEXTUAL STATISTICAL MODEL . . . . . . . . . . . 115 5.1 SYSTEMS AND
CONTEXTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . 115 5.2 INTERFERENCE OF PROBABILITIES: ENSEMBLE DERIVATION
. . . . . . . . . . . . . . . 117 5.3 CLASSICAL AND NONCLASSICAL
PROBABILISTIC BEHAVIORS . . . . . . . . . . . . . . . 122 5.3.1
CLASSICAL PROBABILISTIC BEHAVIOR . . . . . . . . . . . . . . . . . . . .
. . . . 124 5.3.2 QUANTUM PROBABILISTIC BEHAVIOR . . . . . . . . . . . .
. . . . . . . . . . . . 125 5.3.3 NEITHER CLASSICAL NOR QUANTUM
PROBABILISTIC BEHAVIOR . . . . . 127 5.4 HYPERBOLIC PROBABILISTIC
BEHAVIOR . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128 6
LATENT QUANTUM-LIKE STRUCTURE IN THE KOLMOGOROV MODEL . . . . . . . . .
131 6.1 CONTEXTUAL MODEL WITH *CONTINUOUS OBSERVABLES* . . . . . . . . .
. . . . . . 133 6.2 INTERRELATION OF THE MEASURE-THEORETIC AND VAEXJOE
MODELS . . . . . . . . . 134 6.2.1 MEASURE-THEORETIC REPRESENTATION OF
THE VAEXJOE MODEL. . . . . 134 6.2.2 CONTEXTUAL KOLMOGOROV MODEL . . . . .
. . . . . . . . . . . . . . . . . . . 135 CONTENTS XXV 6.3
MEASURE-THEORETIC DERIVATION OF INTERFERENCE . . . . . . . . . . . . . .
. . . . . 136 6.4 QUANTUM-LIKE REPRESENTATION OF THE KOLMOGOROV MODEL .
. . . . . . . . 139 6.5 EXAMPLE OF QUANTUM-LIKE REPRESENTATION OF
CONTEXTUAL KOLMOGOROVIAN MODEL . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . 143 6.5.1 CONTEXTUAL KOLMOGOROVIAN
PROBABILITY MODEL . . . . . . . . . . . . 143 6.5.2 QUANTUM-LIKE
REPRESENTATION . . . . . . . . . . . . . . . . . . . . . . . . . 144 6.6
FEATURES OF QUANTUM-LIKE REPRESENTATION OF CONTEXTUAL KOLMOGOROV MODEL .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . 148 6.7 DISPERSION-FREE STATES . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . 150 6.8 COMPLEX AMPLITUDES OF
PROBABILITIES: MULTI-VALUED VARIABLES . . . . . 151 6.9 VAEXJOE MODELS
WITH MULTI-KOLMOGOROVIAN STRUCTURE . . . . . . . . . . . . . . 157 7
INTERFERENCE OF PROBABILITIES FROM LAW OF LARGE NUMBERS . . . . . . . .
. . 159 7.1 KOLMOGOROVIAN DESCRIPTION OF QUANTUM MEASUREMENTS . . . . .
. . . . . 160 7.2 LIMIT THEOREMS AND FORMULA OF TOTAL PROBABILITY WITH
INTERFERENCE TERM . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . 162 PART III BELL*S INEQUALITY 8
PROBABILISTIC ANALYSIS OF BELL*S ARGUMENT . . . . . . . . . . . . . . .
. . . . . . . . . . 171 8.1 MEASURE-THEORETIC DERIVATIONS OF BELL-TYPE
INEQUALITIES . . . . . . . . . 172 8.1.1 BELL*S INEQUALITY . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172 8.1.2
WIGNER*S INEQUALITY . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . 173 8.1.3 CLAUSER-HORNE-SHIMONY-HOLT*S INEQUALITY . . .
. . . . . . . . . . . . 175 8.2 CORRESPONDENCE BETWEEN CLASSICAL AND
QUANTUM STATISTICAL MODELS 176 8.3 VON NEUMANN POSTULATES ON CLASSICAL *
QUANTUM CORRESPONDENCE 177 8.4 BELL-TYPE NO-GO THEOREMS . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . 179 8.5 RANGE OF
VALUES (*SPECTRAL*) POSTULATE . . . . . . . . . . . . . . . . . . . . .
. . . . 184 XXVI CONTENTS 8.6 CONTEXTUALITY . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185
8.6.1 NON-INJECTIVITY OF CLASSICAL * QUANTUM CORRESPONDENCE . . 186
8.6.2 BELL*S INEQUALITY AND EXPERIMENT . . . . . . . . . . . . . . . . .
. . . . . . 190 8.7 BELL-CONTEXTUALITY AND ACTION AT A DISTANCE . . . .
. . . . . . . . . . . . . . . . 190 9 BELL*S INEQUALITY FOR CONDITIONAL
PROBABILITIES . . . . . . . . . . . . . . . . . . . . . 193 9.1
MEASURE-THEORETIC PROBABILITY MODELS . . . . . . . . . . . . . . . . . .
. . . . . . . 194 9.1.1 CONVENTIONAL PROBABILITY MODEL AND CLASSICAL
STATISTICAL MECHANICS . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . 194 9.1.2 BELL*S PROBABILITY MODEL AND
CLASSICAL STATISTICAL MECHANICS 195 9.1.3 CONFRONTING BELL*S CLASSICAL
PROBABILISTIC MODEL AND QUANTUM MECHANICS . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . 195 9.2 WIGNER-TYPE INEQUALITY FOR
CONDITIONAL PROBABILITIES. . . . . . . . . . . . . 196 9.3 IMPOSSIBILITY
OF CLASSICAL DESCRIPTION OF SPIN OF SINGLE ELECTRON . . . 197 10
FREQUENCY PROBABILISTIC ANALYSIS OF BELL-TYPE CONSIDERATIONS . . . . . .
. 205 10.1 FREQUENCY PROBABILISTIC DESCRIPTION OF HIDDEN VARIABLES . . .
. . . . . . 207 10.2 BELL*S LOCALITY (BELL-CLAUSER-HORNE FACTORABILITY)
CONDITION . . . . . . 211 10.3 CHAOS OF HIDDEN VARIABLES AND FREQUENCIES
FOR MACRO-OBSERVABLES 213 10.4 FLUCTUATING DISTRIBUTIONS OF HIDDEN
VARIABLES . . . . . . . . . . . . . . . . . . . 215 10.5 GENERALIZED
BELL*S INEQUALITY . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . 220 10.6 TRANSMISSION OF INFORMATION WITH THE AID OF
DEPENDENT COLLECTIVES 221 11 ORIGINAL EPR-EXPERIMENT: LOCAL REALISTIC
MODEL . . . . . . . . . . . . . . . . . . 223 11.1 SPACE AND ARGUMENTS
OF EINSTEIN, PODOLSKY, ROSEN, AND BELL . . . . . . 224 11.1.1 BELL*S
LOCAL REALISM . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . 224 11.1.2 EINSTEIN*S LOCAL REALISM . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . 225 11.1.3 LOCAL REALIST REPRESENTATION
FOR QUANTUM SPIN CORRELATIONS 226 11.1.4 EPR VERSUS BOHM AND BELL . . .
. . . . . . . . . . . . . . . . . . . . . . . . . 227 CONTENTS XXVII
11.2 BELL*S THEOREM AND RANGES OF VALUES OF OBSERVABLES . . . . . . . .
. . . 228 11.3 CORRELATION FUNCTIONS IN EPR MODEL . . . . . . . . . . .
. . . . . . . . . . . . . . 229 11.4 SPACE-TIME DEPENDENCE OF
CORRELATION FUNCTIONS AND DISENTANGLEMENT . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . 232 11.4.1
MODIFIED BELL*S EQUATION . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . 232 11.4.2 DISENTANGLEMENT . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . 233 11.5 ROLE OF SPACE-TIME IN EPR
ARGUMENT . . . . . . . . . . . . . . . . . . . . . . . . 236 PART IV
INTERRELATION BETWEEN CLASSICAL AND QUANTUM PROBABILITIES 12 DISCRETE
TIME DYNAMICS . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . 241 12.1 DISCRETE TIME IN NEWTON*S EQUATIONS . . .
. . . . . . . . . . . . . . . . . . . . . . 243 12.2 DIFFRACTION PATTERN
IN A SINGLE SLIT SCATTERING. . . . . . . . . . . . . . . . . . . 244
12.3 INTERFERENCE IN THE TWO-SLIT EXPERIMENT FOR DETERMINISTIC PARTICLES
248 12.4 PHYSICAL INTERPRETATION OF RESULTS OF COMPUTER SIMULATION . . .
. . . . 253 12.5 DISCRETE TIME DYNAMICS . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . 254 12.6 MOTION IN CENTRAL
POTENTIAL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . 256 12.7 ENERGY LEVELS OF THE HYDROGEN ATOM . . . . . . . . . . . .
. . . . . . . . . . . . . 258 12.8 SPECTRUM OF HARMONIC OSCILLATOR . . .
. . . . . . . . . . . . . . . . . . . . . . . . . 261 12.9 GENERAL CASE
OF ARBITRARY SPECTRUM . . . . . . . . . . . . . . . . . . . . . . . . .
. 262 12.10 ENERGY SPECTRUM IN VARIOUS POTENTIALS . . . . . . . . . . .
. . . . . . . . . . . . . 264 12.11 DISCUSSION AND CONCLUSION . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . 265 13
NONCOMMUTATIVE PROBABILITY IN CLASSICAL DISORDERED SYSTEMS . . . . . . .
269 13.1 NONCOMMUTATIVE PROBABILITY AND TIME AVERAGING . . . . . . . . .
. . . . . 270 13.2 NONCOMMUTATIVE PROBABILITY AND DISORDERED SYSTEMS . .
. . . . . . . . . 274 XXVIII CONTENTS 14 DERIVATION OF SCHROEDINGER*S
EQUATION IN THE CONTEXTUAL PROBABILISTIC FRAMEWORK . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 279 14.1
REPRESENTATION OF CONTEXTUAL PROBABILISTIC DYNAMICS IN THE COMPLEX
HILBERT SPACE . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . 281 14.2 SCHROEDINGER DYNAMICS AND COEFFICIENTS OF
SUPPLEMENTARITY . . . . . . 286 PART V HYPERBOLIC QUANTUM MECHANICS 15
REPRESENTATION OF CONTEXTUAL STATISTICAL MODEL BY HYPERBOLIC AMPLITUDES
............................. . . . . . . . . . . . . . . . . . . . . .
. . 293 15.1 HYPERBOLIC ALGEBRA . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . 294 15.2 HYPERBOLIC VERSION OF
QUANTUM-LIKE REPRESENTATION ALGORITHM . . 297 15.2.1 HYPERBOLIC
PROBABILITY AMPLITUDE, HYPERBOLIC BORN*S RULE 297 15.2.2 HYPERBOLIC
HILBERT SPACE . . . . . . . . . . . . . . . . . . . . . . . . . . . .
299 15.2.3 HYPERBOLIC HILBERT SPACE REPRESENTATION . . . . . . . . . . .
. . . . 300 15.3 HYPERBOLIC QUANTIZATION . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . 305 16 HYPERBOLIC QUANTUM
MECHANICS AS DEFORMATION OF CONVENTIONAL CLASSICAL MECHANICS . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . 311 16.1 ON THE CLASSICAL LIMIT OF HYPERBOLIC QUANTUM MECHANICS . .
. . . . . 311 16.2 ULTRA-DISTRIBUTIONS AND PSEUDO-DIFFERENTIAL OPERATORS
OVER THE HYPERBOLIC ALGEBRA . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . 313 16.3 THE CLASSICAL LIMIT OF THE
HYPERBOLIC QUANTUM FIELD THEORY . . . . 320 16.4 HYPERBOLIC FERMIONS AND
HYPERBOLIC SUPERSYMMETRY . . . . . . . . . . . 323 REFERENCES
................................ . . . . . . . . . . . . . . . . . . . .
. . . . . 325 INDEX ................................. . . . . . . . . .
. . . . . . . . . . . . . . . . . . . 349
|
| any_adam_object | 1 |
| author | Khrennikov, Andrei 1958- |
| author_GND | (DE-588)128568410 |
| author_facet | Khrennikov, Andrei 1958- |
| author_role | aut |
| author_sort | Khrennikov, Andrei 1958- |
| author_variant | a k ak |
| building | Verbundindex |
| bvnumber | BV035574054 |
| classification_rvk | SK 800 UK 1200 |
| ctrlnum | (OCoLC)901256227 (DE-599)DNB991181956 |
| dewey-full | 530.12 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530.12 |
| dewey-search | 530.12 |
| dewey-sort | 3530.12 |
| dewey-tens | 530 - Physics |
| discipline | Physik Mathematik Geographie |
| format | Book |
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| id | DE-604.BV035574054 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T21:40:45Z |
| institution | BVB |
| isbn | 9781402095924 ebooks 9781402095931 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-017629583 |
| oclc_num | 901256227 |
| open_access_boolean | |
| owner | DE-384 DE-11 |
| owner_facet | DE-384 DE-11 |
| physical | XXVIII, 353 S. 235 mm x 155 mm |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | Springer |
| record_format | marc |
| series | Fundamental Theories of Physics |
| series2 | Fundamental Theories of Physics |
| spelling | Khrennikov, Andrei 1958- Verfasser (DE-588)128568410 aut Contextual approach to quantum formalism Andrei Khrennikov Berlin Springer 2009 XXVIII, 353 S. 235 mm x 155 mm txt rdacontent n rdamedia nc rdacarrier Fundamental Theories of Physics 160 Quantentheorie Quantum theory Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd rswk-swf Quantenmechanik (DE-588)4047989-4 gnd rswk-swf Quantenmechanik (DE-588)4047989-4 s Wahrscheinlichkeitstheorie (DE-588)4079013-7 s DE-604 Fundamental Theories of Physics 160 (DE-604)BV000012461 160 SWB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017629583&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Khrennikov, Andrei 1958- Contextual approach to quantum formalism Fundamental Theories of Physics Quantentheorie Quantum theory Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd Quantenmechanik (DE-588)4047989-4 gnd |
| subject_GND | (DE-588)4079013-7 (DE-588)4047989-4 |
| title | Contextual approach to quantum formalism |
| title_auth | Contextual approach to quantum formalism |
| title_exact_search | Contextual approach to quantum formalism |
| title_full | Contextual approach to quantum formalism Andrei Khrennikov |
| title_fullStr | Contextual approach to quantum formalism Andrei Khrennikov |
| title_full_unstemmed | Contextual approach to quantum formalism Andrei Khrennikov |
| title_short | Contextual approach to quantum formalism |
| title_sort | contextual approach to quantum formalism |
| topic | Quantentheorie Quantum theory Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd Quantenmechanik (DE-588)4047989-4 gnd |
| topic_facet | Quantentheorie Quantum theory Wahrscheinlichkeitstheorie Quantenmechanik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017629583&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000012461 |
| work_keys_str_mv | AT khrennikovandrei contextualapproachtoquantumformalism |