Heisenberg's uncertainties and the probabilistic interpretation of wave mechanics: with critical notes of the author
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Dordrecht u.a.
Kluwer Acad. Publ.
1990
|
| Schriftenreihe: | Fundamental theories of physics
40 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. 285 - 297 |
| Beschreibung: | XLIV, 302 S. |
| ISBN: | 0792309294 |
Internformat
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| 245 | 1 | 0 | |a Heisenberg's uncertainties and the probabilistic interpretation of wave mechanics |b with critical notes of the author |c by Louis de Broglie |
| 264 | 1 | |a Dordrecht u.a. |b Kluwer Acad. Publ. |c 1990 | |
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Datensatz im Suchindex
| _version_ | 1804119565662158848 |
|---|---|
| adam_text | TABLE OF CONTENTS PREFACE BY ASIM O. BARUT XI FOREWORD BY LOUIS DE
BROGLIE XV THE PROBLEM OF HIDDEN DETERMINISM XIX PREFACE BY GEORGES
LOCHAK XXIII ON THE TRUE IDEAS UNDERLYING WAVE MECHANICS XLI PART ONE
(1950-1951) ON HEISENBERG S UNCERTAINTIES AND THE PROBABILISTIC
INTERPRETATION OF WAVE MECHANICS CHAPTER 1. PRINCIPLES OF WAVE MECHANICS
1. CLASSICAL MECHANICS OF THE POINT MASS. THEORY OF JACOBI 3 2. WAVE
PROPAGATION IN AN ISOTROPIC MEDIUM 7 3. TRANSITION FROM CLASSICAL
MECHANICS TO WAVE MECHANICS 10 4. GENERAL EQUATION FOR THE WAVE
MECHANICS OF A POINT MASS 12 5. AUTOMATIC PROCEDURE FOR OBTAINING THE
WAVE EQUATION 13 CHAPTER 2. PROBABILISTIC INTERPRETATION OF WAVE
MECHANICS 1. INTERPRETATION OF THE PS I WAVE 15 2. PRINCIPLE OF
INTERFERENCE 16 3. PRECISE STATEMENT OF THE PRINCIPLE OF INTERFERENCE.
PROBABILITY FLUID 17 4. THE UNCERTAINTY RELATIONS OF HEISENBERG 18 5.
THE PRINCIPLE OF SPECTRAL DECOMPOSITION (BORN) 21 6. NEW IDEAS RESULTING
FROM THE PRECEDING CONCEPTIONS 22 7. RETURN OF WAVE MECHANICS TO
CLASSICAL MECHANICS. THE THEOREM OF EHRENFEST. GROUP VELOCITY 23 CHAPTER
3. WAVE MECHANICS OF SYSTEMS OF PARTICLES 1. OL D DYNAMICS OF SYSTEMS OF
POINT MASSES 28 2. WAVE MECHANICS OF SYSTEMS OF PARTICLES 30 3.
INTERPRETATION OF WAVE MECHANICS FOR A SYSTEM OF PARTICLES 31 CHAPTER 4-
GENERAL FORMALISM OF WAVE MECHANICS 1. NEW CONCEPTION OF THE QUANTITIES
ATTACHED TO A PARTICLE (OR TO A SYSTEM) 34 2. EIGENVALUES AND
EIGENFUNCTIONS OF A LINEAR HERMITIAN OPERATOR 36 3. CONTINUOUS SPECTRUM
OF THE FREE-PARTICLE HAMILTONIAN. DIRAC S DELTA FUNCTION 39 CHAPTER 5.
GENERAL PRINCIPLES OF THE PROBABILISTIC INTERPRETATION OF WAVE MECHANICS
1. GENERAL IDEAS 42 2. THE ALGEBRAIC MATRICES AND THEIR PROPERTIES 46 3.
OPERATORS AND MATRICES IN WAVE MECHANICS 48 4. MEAN VALUES AND
DISPERSIONS IN WAVE MECHANICS 49 5. FIRST INTEGRALS IN WAVE MECHANICS 51
6. ANGULAR MOMENTUM IN WAVE MECHANICS 53 CHAPTER 6. THEORY OF THE
COMMUTATION OF OPERATORS IN WAVE MECHANICS 1. GENERAL THEOREMS 55 2.
COROLLARIES OF THE FOREGOING THEOREMS 60 3. SIMULTANEOUS MEASUREMENT OF
TWO QUANTITIES IN WAVE MECHANICS 63 4. EXAMPLES OF QUANTITIES THAT ARE
NOT SIMULTANEOUSLY MEASURABLE. DISTINCTION BETWEEN TWO KINDS OF
NON-COMMUTATION 66 CHAPTER 7. PHYSICAL IMPOSSIBILITY OF SIMULTANEOUSLY
MEASURING CANONICALLY CONJUGATE QUANTITIES 1. NECESSITY TO EXAMINE THE
IMPOSSIBILITY OF SIMULTANEOUSLY AND PRECISELY MEASURING TWO CANONICALLY
CONJUGATE QUANTITIES 68 2. THE HEISENBERG MICROSCOPE 69 3. MEASUREMENT
OF THE SPEED OF AN ELECTRON BY MEANS OF THE DOPPLER EFFECT 71 4. PASSAGE
OF A PARTICLE THROUGH A RECTANGULAR APERTURE 73 5. IMPORTANT REMARK ON
THE MEASUREMENT OF SPEED 76 6. THE CASE OF TWO OPERATORS WITH A NONZERO
COMMUTATOR 77 7. BOHR S COMPLEMENTARITY 79 8. BOHR S CALCULATION FOR
YOUNG S SLITS 81 CHAPTER 8. PRECISE FORM OF THE UNCERTAINTY RELATIONS 1.
THEOREM ABOUT THE DISPERSION OF NON-COMMUTING QUANTITIES 85 2. OPTIMAL
NATURE OF THE GAUSSIAN WAVE PACKET 90 3. COMPARISON OF THE THEOREM ON
DISPERSIONS WITH THE QUALITATIVE UNCERTAINTY RELATIONS OF HEISENBERG
(PAULI AND ROBERTSON) 94 4. VARIOUS CONSIDERATIONS ABOUT UNCERTAINTIES.
SHARP-EDGED UNCERTAINTIES 95 CHAPTER 9. HEISENBERG S FOURTH UNCERTAINTY
RELATION 1. THE ABSENCE OF SYMMETRY BETWEEN SPACE AND TIME IN WAVE
MECHANICS 103 2. CORRECT FORMULATION OF THE FOURTH UNCERTAINTY RELATION
105 3. ILLUSTRATION OF THE PRECEDING DEFINITION 105 4. VARIOUS REMARKS
ABOUT THE FOURTH UNCERTAINTY RELATION 108 5. METHOD OF VARIATION OF
CONSTANTS. TRANSITION PROBABILITY 110 6. TRANSITION PROBABILITIES 114 7.
UNCERTAINTY RELATIONS AND RELATIVITY THEORY 117 8. FORMULAS OF
MANDELSTAM AND TAMM 121 CHAPTER 10. EXAMINATION OF SOME DIFFICULT POINTS
IN WAVE MECHANICS 1. REDUCTION OF THE PROBABILITY PACKET BY MEASUREMENT
124 2. IMPOSSIBILITY OF DISCOVERING THE ANTERIOR STATE OF A MEASUREMENT
FROM ITS POSTERIOR STATE. EFFACEMENT OF PHASES BY MEASUREMENT 125 3.
POSSIBILITY OF DISCOVERING THE PAST, STARTING FROM A MEASUREMENT MADE AT
A GIVEN INSTANT (POSTDICTION) 127 4. INTERFERENCE OF PROBABILITIES 129
5. SOME CONSEQUENCES OF THE DISAPPEARANCE OF THE TRAJECTORY CONCEPT 132
6. DISCUSSIONS CONCERNING CORRELATED SYSTEMS 136 7. COMPLEMENTARY
REMARKS ON THE EINSTEIN-BOHR CONTROVERSY 143 PART TWO (1951-1952) ON THE
PROBABILISTIC INTERPRETATION OF WAVE MECHANICS AND VARIOUS RELATED
QUESTIONS CHAPTER 11. SUMMARY OF SOME GENERAL CONCEPTS OF PROBABILITY
CALCULUS 1. PROBABILITY LAWS FOR ONE VARIABLE. DISTRIBUTION FUNCTION 153
2. PROBABILITY LAWS FOR TWO VARIABLES 159 3. VERY IMPORTANT REMARK
CONCERNING THE FOREGOING RESULTS 166 CHAPTER 12. RECALLING THE GENERAL
CONCEPTS OF WAVE MECHANICS 1. THE INTERFERENCE PRINCIPLE. THEORY OF THE
PILOT WAVE 173 CHAPTER 13. INTRODUCTION OF THE CHARACTERISTIC FUNCTION
INTO THE PROBABILITY FORMALISM OF WAVE MECHANICS 1. CHARACTERISTIC
FUNCTION FOR A SINGLE QUANTITY 180 2. CHARACTERISTIC FUNCTION FOR TWO
COMMUTING QUANTITIES 186 3. CORRELATION COEFFICIENT. MARGINAL LAWS 187
4. GENERAL THEOREMS OF WAVE MECHANICS CONSIDERED FROM THE
CHARACTERISTIC-FUNCTION POINT OF VIEW 190 5. CASE OF TWO NONCOMMUTING
QUANTITIES 197 (A) REMINDER ABOUT THE REDUCTION OF THE PROBABILITY
PACKET BY MEASUREMENT 197 (B) INTERFERENCE OF PROBABILITIES 198 (C) THE
DISTRIBUTION FUNCTION RHO (X,P X ) OF WIGNER AND BASS 201 (D) THE
WIGNER-BASS DENSITY RHO (X,P X ) AND THE HYDRODYNAMIC INTERPRETATION OF
WAVE MECHANICS 207 (E) YVON S THEORY 213 CHAPTER 1 . THEORY OF MIXTURES
AND VON NEUMANN S THEORY OF MEASUREMENT 1. MIXTURES AND PURE CASES 220
2. VON NEUMANN S STATISTICAL MATRIX FOR A PURE CASE 224 3. THE
STATISTICAL MATRIX FOR A MIXTURE OF PURE CASES 227 4. IRREDUCIBILITY OF
PURE CASES 230 5. IMPOSSIBILITY OF REDUCING THE LAWS OF WAVE MECHANICS
TO A HIDDEN DETERMINISM (VON NEUMANN) 232 CHAPTER 15. MEASUREMENT THEORY
IN WAVE MECHANICS 1. GENERALITIES 238 2. STATISTICS OF TWO INTERACTING
SYSTEMS 239 3. CORRELATION COEFFICIENTS IN THE INTERACTION BETWEEN TWO
QUANTUM SYSTEMS 243 4. MEASUREMENT OF A QUANTITY 244 5. EXAMPLE OF A
MEASURING EXPERIMENT 249 6. DIVERSE REMARKS ON MEASUREMENT 253 7.
THERMODYNAMICAL CONSIDERATIONS (VON NEUMANN) 259 8. REVERSIBLE AND
IRREVERSIBLE EVOLUTIONS 263 9. THE STATISTICAL MATRIX P 0 266 CHAPTER
16. THE ROLE OF TIME IN WAVE MECHANICS 1. RETRODICTION ACCORDING TO
COSTA DE BEAUREGARD 268 2. SPECIAL ROLE OF TIME IN QUANTUM MECHANICS.
THE FOURTH UNCERTAINTY RELATION 273 3. CORRECT STATEMENT OF THE FOURTH
UNCERTAINTY RELATION 275 4. THE FOURTH UNCERTAINTY RELATION AND
PERTURBATION THEORY 276 5. THE OPERATORS H AND (H/2PI)D/DT 279 6.
APPLICATION OF THE FORMALISM OF ARNOUS TO THE OPERATORS ACTING ON TIME
280 7. MULTITEMPORAL FORMALISM. MULTIPLICITY CURVES IN SPACETIME 283
WORKS OF LOUIS DE BROGLIE 285 INDEX
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| isbn | 0792309294 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-003349795 |
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| physical | XLIV, 302 S. |
| publishDate | 1990 |
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| publisher | Kluwer Acad. Publ. |
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| series | Fundamental theories of physics |
| series2 | Fundamental theories of physics |
| spelling | Broglie, Louis de 1892-1987 Verfasser (DE-588)118674293 aut Les incertitudes d'Heisenberg et l'interprétation probabiliste de la mécanique ondulatoire Heisenberg's uncertainties and the probabilistic interpretation of wave mechanics with critical notes of the author by Louis de Broglie Dordrecht u.a. Kluwer Acad. Publ. 1990 XLIV, 302 S. txt rdacontent n rdamedia nc rdacarrier Fundamental theories of physics 40 Literaturverz. S. 285 - 297 Broglie, Louis de 1892-1987 (DE-588)118674293 gnd rswk-swf Wahrscheinlichkeitstheorie - Deutung - Wellenmechanik - Unschärferelation Quantentheorie (DE-588)4047992-4 gnd rswk-swf Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd rswk-swf Wellenmechanik (DE-588)4127857-4 gnd rswk-swf Interpretation (DE-588)4072905-9 gnd rswk-swf Unschärferelation (DE-588)4186953-9 gnd rswk-swf (DE-588)4006432-3 Bibliografie gnd-content Quantentheorie (DE-588)4047992-4 s Interpretation (DE-588)4072905-9 s DE-604 Unschärferelation (DE-588)4186953-9 s DE-188 Wellenmechanik (DE-588)4127857-4 s Wahrscheinlichkeitstheorie (DE-588)4079013-7 s Broglie, Louis de 1892-1987 (DE-588)118674293 p Fundamental theories of physics 40 (DE-604)BV000012461 40 OEBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003349795&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Broglie, Louis de 1892-1987 Heisenberg's uncertainties and the probabilistic interpretation of wave mechanics with critical notes of the author Fundamental theories of physics Broglie, Louis de 1892-1987 (DE-588)118674293 gnd Wahrscheinlichkeitstheorie - Deutung - Wellenmechanik - Unschärferelation Quantentheorie (DE-588)4047992-4 gnd Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd Wellenmechanik (DE-588)4127857-4 gnd Interpretation (DE-588)4072905-9 gnd Unschärferelation (DE-588)4186953-9 gnd |
| subject_GND | (DE-588)118674293 (DE-588)4047992-4 (DE-588)4079013-7 (DE-588)4127857-4 (DE-588)4072905-9 (DE-588)4186953-9 (DE-588)4006432-3 |
| title | Heisenberg's uncertainties and the probabilistic interpretation of wave mechanics with critical notes of the author |
| title_alt | Les incertitudes d'Heisenberg et l'interprétation probabiliste de la mécanique ondulatoire |
| title_auth | Heisenberg's uncertainties and the probabilistic interpretation of wave mechanics with critical notes of the author |
| title_exact_search | Heisenberg's uncertainties and the probabilistic interpretation of wave mechanics with critical notes of the author |
| title_full | Heisenberg's uncertainties and the probabilistic interpretation of wave mechanics with critical notes of the author by Louis de Broglie |
| title_fullStr | Heisenberg's uncertainties and the probabilistic interpretation of wave mechanics with critical notes of the author by Louis de Broglie |
| title_full_unstemmed | Heisenberg's uncertainties and the probabilistic interpretation of wave mechanics with critical notes of the author by Louis de Broglie |
| title_short | Heisenberg's uncertainties and the probabilistic interpretation of wave mechanics |
| title_sort | heisenberg s uncertainties and the probabilistic interpretation of wave mechanics with critical notes of the author |
| title_sub | with critical notes of the author |
| topic | Broglie, Louis de 1892-1987 (DE-588)118674293 gnd Wahrscheinlichkeitstheorie - Deutung - Wellenmechanik - Unschärferelation Quantentheorie (DE-588)4047992-4 gnd Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd Wellenmechanik (DE-588)4127857-4 gnd Interpretation (DE-588)4072905-9 gnd Unschärferelation (DE-588)4186953-9 gnd |
| topic_facet | Broglie, Louis de 1892-1987 Wahrscheinlichkeitstheorie - Deutung - Wellenmechanik - Unschärferelation Quantentheorie Wahrscheinlichkeitstheorie Wellenmechanik Interpretation Unschärferelation Bibliografie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003349795&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000012461 |
| work_keys_str_mv | AT broglielouisde lesincertitudesdheisenbergetlinterpretationprobabilistedelamecaniqueondulatoire AT broglielouisde heisenbergsuncertaintiesandtheprobabilisticinterpretationofwavemechanicswithcriticalnotesoftheauthor |