Group theoretical foundations of quantum mechanics:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Commack, NY
Nova Science Publ.
1995
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIII, 263 S. |
| ISBN: | 1560722487 |
Staff View
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Record in the Search Index
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| adam_text | THEORETICAL FOUNDATIONS OF QUANTUM MECHANICS R. MIRMAN NOVA SCIENCE
PUBLISHERS, INC. TABLE OF CONTENTS PREFACE V FOUNDATIONS 1 1.1 GEOMETRY,
PHYSICS, NECESSITY 1 1.2 NATURE IS QUANTUM MECHANICAL: WHY? 2 1.3 THE
FOUNDATIONS OF THE TERMINOLOGY 3 1.3.1 FRAMEWORKS AND DESCRIPTIONS 3
1.3.2 HOW OBJECTS MUST BE DESCRIBED * AND WHAT THIS IMPLIES . 4 1.3.3
THEORIES FUNDAMENTAL AND THEORIES PHENOMENOLOGICAL . . 5 1.4 WHAT IS A
POSSIBLE FRAMEWORK FOR PHYSICS? 7 1.4.1 THE POINCARE GROUP AND PRODUCTS
OF ITS REPRESENTATIONS . 9 1.4.2 THE ARGUMENTS DO NOT DEPEND ON
INVARIANCE 10 1.4.3 GEOMETRY, NOT SYMMETRY, ELIMINATES CLASSICAL PHYSICS
... 11 1.4.4 OBJECTS ARE GIVEN BY FUNCTIONS, AND THIS IS QUANTUM ME-
CHANICS 13 1.5 THE POVERTY OF A COMPLETELY CLASSICAL PHYSICS 14 1.5.1 IS
A COMPLETELY CLASSICAL PHYSICS POSSIBLE? 15 1.5.2 CLASSICAL PHYSICS IN
AN ENCLOSED TUBE 18 1.6 IS ELECTROSTATIC ENERGY INFINITE IN QUANTUM
MECHANICS? 19 1.7 FUNDAMENTAL ASSUMPTIONS AND CONSEQUENCES 22 WHY
GEOMETRY, SO PHYSICS, REQUIRE COMPLEX NUMBERS 25 2.1 WHAT NUMBERS MUST
GEOMETRY AND PHYSICS USE? 25 2.1.1 THE PREEMINENCE OF COMPLEX NUMBERS IN
GEOMETRY AND PHYSICS 25 2.1.2 HOW TRANSLATIONS INTRODUCE COMPLEX NUMBERS
26 2.1.3 TRANSLATIONS MUST BE APPLIED TO FUNCTIONS, COMPLEX ONES . 28
2.1.4 ROTATIONS ALSO GIVE COMPLEX NUMBERS 28 2.1.5 LIE GROUPS REQUIRE
COMPLEX NUMBERS 29 2.2 SPACE MUST BE REAL, STATEFUNCTIONS COMPLEX 32
2.2.1 THE NATURE OF EUCLIDEAN GEOMETRY 32 2.2.2 STATEFUNCTIONS ARE
COMPLEX 35 IX CONTENTS 2.3 THE NATURE OF THE UNIVERSE AND THE NUMBERS 36
PROPERTIES OF STATEFUNCTIONS 38 3.1 IS IT A WAVE OR IS IT A PARTICLE? 38
3.1.1 HOW PARTICLE ASPECTS SEEM TO ARISE EXPERIMENTALLY 38 3.1.2 DO
CLOUD-CHAMBER TRACKS IMPLY PARTICLES? 40 3.1.3 OBJECTS ARE NOT WAVES 41
3.1.4 THE CORRECT DESCRIPTION IS THAT OF FUNCTIONS 42 3.2 HOW TO REDUCE
A STATEFUNCTION 42 3.2.1 WAVEFUNCTION COLLAPSE IN A CLOUD CHAMBER 43
3.2.2 DOES DECAY CAUSE COLLAPSE ? 46 3.2.3 THE PROCESS OF REDUCTION IS
GIVEN BY SCHRODINGER S EQUATION 46 3.3 HOW STATEFUNCTIONS GIVE
PROBABILITY 47 3.3.1 WHY GROUP PROPERTIES REQUIRE A STATISTICAL
INTERPRETATION . 47 3.3.2 DIFFERENT WAYS OF GIVING FREQUENCY ARE
EQUIVALENT 48 3.3.3 PROBABILITY IS GIVEN BY THE SQUARE OF THE
STATEFUNCTION ... 49 3.3.4 THE PROBABILITY DEPENDS ON THE ABSOLUTE
SQUARE 51 3.4 STATEFUNCTIONS AND EIGENVALUES 52 3.4.1 THE UNCERTAINTY
PRINCIPLE 52 3.4.2 WHY OBSERVABLES ARE EIGENVALUES 53 3.4.3 STATE LABELS
ARE CONSERVED 55 3.4.4 WHY STATEFUNCTIONS ARE EIGENFUNCTIONS OF GROUP
INVARIANTS 56 THE FOUNDATIONS OF COHERENT SUPERPOSITION 58 4.1
LINEARITY, SUPERPOSITION AND GROUP REPRESENTATIONS ..58 4.1.1 WHAT DOES
COHERENT SUPERPOSITION MEAN? 59 4.1.2 SUPERPOSITION IS REQUIRED BY
COMPACT GROUPS 60 4.1.3 WHY THE ARGUMENTS DIFFER FOR NONCOMPACT GROUPS
62 4.2 ARBITRARY SUPERPOSITIONS 63 4.2.1 LOCALIZATION LEADS TO COHERENT
SUPERPOSITION 63 4.2.2 EXPERIMENTAL MEANING OF COHERENT SUPERPOSITION 64
4.2.3 POSSIBLE SUMS MAY NOT BE EXPERIMENTALLY SO 66 4.3 WHAT GETS ADDED?
67 4.4 WHEN NEED LINEARITY HOLD, AND WHEN CAN IT BREAK DOWN? 69 4.4.1
WHAT IS THE EFFECT OF NONLINEARITY? 69 4.4.2 HOW DO ABELIAN GROUPS
DIFFER? 71 4.4.3 HOW THE TYPE OF GROUP AFFECTS THE TYPE OF LABELS 72
4.4.4 LINEARITY AND THE POINCARE GROUP 73 4.5 GRAVITATION AND
SUPERPOSITION 74 4.5.1 GRAVITATIONAL BASIS STATES 74 4.5.2 ARE COHERENT
SUPERPOSITION AND GRAVITATION COMPATIBLE? . 76 4.5.3 THE UNCERTAINTY
PRINCIPLE AND GRAVITATION 77 4.5.4 IS GRAVITATIONAL PHASE MEANINGFUL? 78
CONTENTS 4.5.5 ARE COLLIDING GRAVITATIONAL WAVES SOLUTIONS? 78 4.6
LINEARITY AND INTERACTIONS 79 4.7 PROBABILITY AND LINEARITY 80 4.7.1
PROBABILITY AND GRAVITATION 81 4.7.2 GRAVITATION ILLUSTRATES OTHER
PROBLEMS FROM NONLINEARITY . 82 4.7.3 GRAVITATION IS A MODEL FOR THE
EFFECTS OF INTERACTIONS .... 83 GEOMETRY, TRANSFORMATIONS, GROUPS AND
OBSERVERS 85 5.1 TRANSFORMATIONS ARE PHYSICS: PHYSICS IS TRANSFORMA-
TIONS 85 5.1.1 WHAT ARE THESE TRANSFORMATIONS? 86 5.1.2 THE NEED FOR
OBSERVERS 87 5.1.3 WHAT ARE OBSERVERS? 88 5.1.4 WHAT EQUATIONS GOVERN
PHYSICAL OBJECTS? 89 5.2 OBSERVATIONS MUST BE CONSISTENT - AND THIS IS
SUFFICIENT 90 5.2.1 THE STRINGENCY OF CONSISTENCY 91 5.2.2
TRANSFORMATIONS ARE EXPRESSIBLE AS PRODUCTS 91 5.2.3 BEHAVIOR IN
IDENTICAL SITUATIONS MUST BE HISTORY-INDEPEND- ENT 93 5.2.4 HOW
ELECTRONS RELATE THEN-OBSERVATIONS 94 5.2.5 MATHEMATICAL RESTRICTIONS ON
OBSERVERS, OBSERVATIONS AND EQUATIONS 96 5.2.6 TRANSFORMATIONS RESTRICT
GOVERNING EQUATIONS 99 5.3 GEOMETRY RESTRICTS PHYSICS 100 5.3.1 WHY
PHYSICAL OBJECTS ARE DESCRIBED BY BASIS VECTORS .... 101 5.3.2 WHY
GEOMETRICALLY IS THE POINCARE GROUP REQUIRED? 103 5.3.3 THE NECESSITY
FOR POINCARE BASIS VECTORS 104 5.3.4 TRANSFORMATIONS OF OBSERVERS
INTERACTING WITH OBJECTS . . 106 5.3.5 ALGEBRA, GEOMETRY, BASIS STATES,
STATEFUNCTIONS 107 THE POINCARE GROUP AND ITS IMPLICATIONS 108 6.1
INHOMOGENEOUS GROUPS 108 6.2 THE POINCARE GROUP 110 6.2.1
REPRESENTATIONS OF THE POINCARE GROUP 110 6.2.2 LORENTZ-SUBGROUP
REPRESENTATIONS 110 6.2.3 PRODUCTS OF POINCARE REPRESENTATIONS 113 6.3
THE MEANING AND IMPLICATIONS OF THE DIRAC EQUATION . . 114 6.3.1 THE
REPRESENTATIONS GIVING THE DIRAC EQUATION 115 6.3.2 WHY THERE IS AN
EQUATION OF MOTION FOR SPIN-1, ONLY .... 116 6.3.3 SCHRODINGER S
EQUATION, NEWTON S LAW, HAMILTONIANS, LAGRANGIANS 118 6.4 DOES THE
PROTON HAVE INTERNAL STRUCTURE? 119
|
| any_adam_object | 1 |
| author | Mirman, Ronald |
| author_facet | Mirman, Ronald |
| author_role | aut |
| author_sort | Mirman, Ronald |
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| building | Verbundindex |
| bvnumber | BV011096623 |
| classification_rvk | UK 3000 |
| ctrlnum | (OCoLC)247120307 (DE-599)BVBBV011096623 |
| discipline | Physik |
| format | Book |
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| indexdate | 2024-07-09T18:03:55Z |
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| isbn | 1560722487 |
| language | English |
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| physical | XIII, 263 S. |
| publishDate | 1995 |
| publishDateSearch | 1995 |
| publishDateSort | 1995 |
| publisher | Nova Science Publ. |
| record_format | marc |
| spelling | Mirman, Ronald Verfasser aut Group theoretical foundations of quantum mechanics R. Mirman Commack, NY Nova Science Publ. 1995 XIII, 263 S. txt rdacontent n rdamedia nc rdacarrier Gruppentheorie (DE-588)4072157-7 gnd rswk-swf Quantenmechanik (DE-588)4047989-4 gnd rswk-swf Quantenmechanik (DE-588)4047989-4 s Gruppentheorie (DE-588)4072157-7 s DE-604 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007433605&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Mirman, Ronald Group theoretical foundations of quantum mechanics Gruppentheorie (DE-588)4072157-7 gnd Quantenmechanik (DE-588)4047989-4 gnd |
| subject_GND | (DE-588)4072157-7 (DE-588)4047989-4 |
| title | Group theoretical foundations of quantum mechanics |
| title_auth | Group theoretical foundations of quantum mechanics |
| title_exact_search | Group theoretical foundations of quantum mechanics |
| title_full | Group theoretical foundations of quantum mechanics R. Mirman |
| title_fullStr | Group theoretical foundations of quantum mechanics R. Mirman |
| title_full_unstemmed | Group theoretical foundations of quantum mechanics R. Mirman |
| title_short | Group theoretical foundations of quantum mechanics |
| title_sort | group theoretical foundations of quantum mechanics |
| topic | Gruppentheorie (DE-588)4072157-7 gnd Quantenmechanik (DE-588)4047989-4 gnd |
| topic_facet | Gruppentheorie Quantenmechanik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007433605&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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