Variational principles in physics:
Saved in:
| Main Author: | |
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| Format: | Book |
| Language: | English |
| Published: |
New York, NY
Springer
2007
|
| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Physical Description: | X, 183 S. Ill., graph. Darst. |
| ISBN: | 9780387377476 0387377476 0387377484 9780387377483 |
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| 245 | 1 | 0 | |a Variational principles in physics |c Jean-Louis Basdevant |
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| 650 | 4 | |a Variational principles | |
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JEAN-LOUIS BASDEVANT VARIATIONAL PRINCIPLES IN PHYSICS 4Y SPRINGER
CONTENTS PREFACE V 1 INTRODUCTION 1 1.1 ESTHETICS AND PHYSICS 1 1.2
METAPHYSICS AND SCIENCE 3 1.3 NUMBERS, MUSIC, AND QUANTUM PHYSICS 4 1.4
THE AGE OF ENLIGHTENMENT AND THE PRINCIPLE OF THE BEST 7 1.5 THE FERMAT
PRINCIPLE AND ITS CONSEQUENCES 8 1.6 VARIATIONAL PRINCIPLES 9 1.7 THE
MODERN ERA, FROM LAGRANGE TO EINSTEIN AND FEYNMAN. . 12 2 VARIATIONAL
PRINCIPLES 21 2.1 THE FERMAT PRINCIPLE AND VARIATIONAL CALCULUS 22 2.1.1
LEAST TIME PRINCIPLE 22 2.1.2 VARIATIONAL CALCULUS OF EULER AND LAGRANGE
26 2.1.3 MIRAGES AND CURVED RAYS 27 2.2 EXAMPLES OF THE PRINCIPLE OF
NATURAL ECONOMY 30 2.2.1 MAUPERTUIS PRINCIPLE 30 2.2.2 SHAPE OF A
MASSIVE STRING 31 2.2.3 KIRCHHOFF'S LAWS 32 2.2.4 ELECTROSTATIC
POTENTIAL 33 2.2.5 SOAP BUBBLES 34 2.3 THERMODYNAMIC EQUILIBRIUM:
PRINCIPLE OF MAXIMAL DISORDER . . 35 2.3.1 PRINCIPLE OF EQUAL
PROBABILITY OF STATES 35 2.3.2 MOST PROBABLE DISTRIBUTION AND
EQUILIBRIUM 36 2.3.3 LAGRANGE MULTIPLIERS 37 2.3.4 BOLTZMANN FACTOR 38
2.3.5 EQUALIZATION OF TEMPERATURES 39 2.3.6 THE IDEAL GAS 40 2.3.7
BOLTZMANN'S ENTROPY 41 2.3.8 HEAT AND WORK 42 VIII CONTENTS 2.4 PROBLEMS
43 3 THE ANALYTICAL MECHANICS OF LAGRANGE 47 3.1 LAGRANGIAN FORMALISM
AND THE LEAST ACTION PRINCIPLE 49 3.1.1 LEAST ACTION PRINCIPLE 49 3.1.2
LAGRANGE-EULER EQUATIONS 50 3.1.3 OPERATION OF THE OPTIMIZATION
PRINCIPLE 52 3.2 INVARIANCES AND CONSERVATION LAWS 53 3.2.1 CONJUGATE
MOMENTA AND GENERALIZED MOMENTA 53 3.2.2 CYCLIC VARIABLES 54 3.2.3
ENERGY AND TRANSLATIONS IN TIME 54 3.2.4 MOMENTUM AND TRANSLATIONS IN
SPACE 56 3.2.5 ANGULAR MOMENTUM AND ROTATIONS 57 3.2.6 DYNAMICAL
SYMMETRIES 57 3.3 VELOCITY-DEPENDENT FORCES 58 3.3.1 DISSIPATIVE SYSTEMS
58 3.3.2 LORENTZ FORCE 59 3.3.3 GAUGE INVARIANCE 60 3.3.4 MOMENTUM 61
3.4 LAGRANGIAN OF A RELATIVISTIC PARTICLE 61 3.4.1 FREE PARTICLE 61
3.4.2 ENERGY AND MOMENTUM 62 3.4.3 INTERACTION WITH AN ELECTROMAGNETIC
FIELD 63 3.5 PROBLEMS :. 65 4 HAMILTON'S CANONICAL FORMALISM 67 4.1
HAMILTON'S CANONICAL FORMALISM 68 4.1.1 CANONICAL EQUATIONS 69 4.2
DYNAMICAL SYSTEMS 70 4.2.1 POINCARE AND CHAOS IN THE SOLAR SYSTEM 71
4.2.2 THE BUTTERFLY EFFECT AND THE LORENZ ATTRACTOR 71 4.3 POISSON
BRACKETS AND PHASE SPACE 73 4.3.1 TIME EVOLUTION AND CONSTANTS OF THE
MOTION 74 4.3.2 CANONICAL TRANSFORMATIONS 75 4.3.3 PHASE SPACE;
LIOUVILLE'S THEOREM 78 4.3.4 ANALYTICAL MECHANICS AND QUANTUM MECHANICS
80 4.4 CHARGED PARTICLE IN AN ELECTROMAGNETIC FIELD 81 4.4.1 HAMILTONIAN
81 4.4.2 GAUGE INVARIANCE 82 4.5 THE ACTION AND THE HAMILTON-JACOBI
EQUATION 82 4.5.1 THE ACTION AS A FUNCTION OF THE COORDINATES AND TIME
83 4.5.2 THE HAMILTON-JACOBI EQUATION AND JACOBI THEOREM . 85 4.5.3
CONSERVATIVE SYSTEMS, THE REDUCED ACTION, AND THE MAUPERTUIS PRINCIPLE
87 4.6 ANALYTICAL MECHANICS AND OPTICS 89 CONTENTS IX 4.6.1 GEOMETRIC
LIMIT OF WAVE OPTICS 89 4.6.2 SEMICLASSICAL APPROXIMATION IN QUANTUM
MECHANICS . 91 4.7 PROBLEMS 92 LAGRANGIAN FIELD THEORY 97 5.1
VIBRATING STRING 98 5.2 FIELD EQUATIONS 99 5.2.1 GENERALIZED
LAGRANGE-EULER EQUATIONS 99 5.2.2 HAMILTONIAN FORMALISM 100 5.3 SCALAR
FIELD 101 5.4 ELECTROMAGNETIC FIELD 102 5.5 EQUATIONS OF FIRST ORDER IN
TIME 104 5.5.1 DIFFUSION EQUATION 104 5.5.2 SCHRODINGER EQUATION 104 5.6
PROBLEMS 105 MOTION IN A CURVED SPACE 107 6.1 CURVED SPACES 108 6.1.1
GENERALITIES 108 6.1.2 METRIC TENSOR 110 6.1.3 EXAMPLES ILL 6.2 FREE
MOTION IN A CURVED SPACE 112 6.2.1 LAGRANGIAN 113 6.2.2 EQUATIONS OF
MOTION 113 6.2.3 SIMPLE EXAMPLES 114 6.2.4 CONJUGATE MOMENTA AND THE
HAMILTONIAN 117 6.3 GEODESIC LINES 117 6.3.1 DEFINITION 117 6.3.2
EQUATION OF THE GEODESIES 118 6.3.3 EXAMPLES 119 6.3.4 MAUPERTUIS
PRINCIPLE AND GEODESIES 121 6.4 GRAVITATION AND THE CURVATURE OF
SPACE-TIME 122 6.4.1 NEWTONIAN GRAVITATION AND RELATIVITY 122 6.4.2 THE
SCHWARZSCHILD METRIC 124 6.4.3 GRAVITATION AND TIME FLOW 125 6.4.4
PRECESSION OF MERCURY'S PERIHELION 125 6.4.5 GRAVITATIONAL DEFLECTION OF
LIGHT RAYS 130 6.5 GRAVITATIONAL OPTICS AND MIRAGES _. 133 6.5.1
GRAVITATIONAL LENSING 133 6.5.2 GRAVITATIONAL MIRAGES 134 6.5.3 BARYONIC
DARK MATTER 139 6.6 PROBLEMS 144 X CONTENTS 7 FEYNMAN'S PRINCIPLE IN
QUANTUM MECHANICS 145 7.1 FEYNMAN'S PRINCIPLE 146 7.1.1 RECOLLECTIONS OF
ANALYTICAL MECHANICS 146 7.1.2 QUANTUM AMPLITUDES 147 7.1.3
SUPERPOSITION PRINCIPLE AND FEYNMAN'S PRINCIPLE 147 7.1.4 PATH INTEGRALS
148 7.1.5 AMPLITUDE OF SUCCESSIVE EVENTS 150 7.2 FREE PARTICLE 152 7.2.1
PROPAGATOR OF A FREE PARTICLE 152 7.2.2 EVOLUTION EQUATION OF THE FREE
PROPAGATOR 154 7.2.3 NORMALIZATION AND INTERPRETATION OF THE PROPAGATOR.
. . . 155 7.2.4 FOURIER AND SCHRODINGER EQUATIONS 155 7.2.5 ENERGY AND
MOMENTUM 156 7.2.6 INTERFERENCE AND DIFFRACTION 157 7.3 WAVE FUNCTION
AND THE SCHRODINGER EQUATION 157 7.3.1 FREE PARTICLE 158 7.3.2 PARTICLE
IN A POTENTIAL 159 7.4 CONCLUDING REMARKS 161 7.4.1 CLASSICAL LIMIT 161
7.4.2 ENERGY AND MOMENTUM 162 7.4.3 OPTICS AND ANALYTICAL MECHANICS 163
7.4.4 THE ESSENCE OF THE PHASE 163 7.5 PROBLEMS 164 SOLUTIONS 167
REFERENCES 179 INDEX 181 |
| adam_txt |
JEAN-LOUIS BASDEVANT VARIATIONAL PRINCIPLES IN PHYSICS 4Y SPRINGER
CONTENTS PREFACE V 1 INTRODUCTION 1 1.1 ESTHETICS AND PHYSICS 1 1.2
METAPHYSICS AND SCIENCE 3 1.3 NUMBERS, MUSIC, AND QUANTUM PHYSICS 4 1.4
THE AGE OF ENLIGHTENMENT AND THE PRINCIPLE OF THE BEST 7 1.5 THE FERMAT
PRINCIPLE AND ITS CONSEQUENCES 8 1.6 VARIATIONAL PRINCIPLES 9 1.7 THE
MODERN ERA, FROM LAGRANGE TO EINSTEIN AND FEYNMAN. . 12 2 VARIATIONAL
PRINCIPLES 21 2.1 THE FERMAT PRINCIPLE AND VARIATIONAL CALCULUS 22 2.1.1
LEAST TIME PRINCIPLE 22 2.1.2 VARIATIONAL CALCULUS OF EULER AND LAGRANGE
26 2.1.3 MIRAGES AND CURVED RAYS 27 2.2 EXAMPLES OF THE PRINCIPLE OF
NATURAL ECONOMY 30 2.2.1 MAUPERTUIS PRINCIPLE 30 2.2.2 SHAPE OF A
MASSIVE STRING 31 2.2.3 KIRCHHOFF'S LAWS 32 2.2.4 ELECTROSTATIC
POTENTIAL 33 2.2.5 SOAP BUBBLES 34 2.3 THERMODYNAMIC EQUILIBRIUM:
PRINCIPLE OF MAXIMAL DISORDER . . 35 2.3.1 PRINCIPLE OF EQUAL
PROBABILITY OF STATES 35 2.3.2 MOST PROBABLE DISTRIBUTION AND
EQUILIBRIUM 36 2.3.3 LAGRANGE MULTIPLIERS 37 2.3.4 BOLTZMANN FACTOR 38
2.3.5 EQUALIZATION OF TEMPERATURES 39 2.3.6 THE IDEAL GAS 40 2.3.7
BOLTZMANN'S ENTROPY 41 2.3.8 HEAT AND WORK 42 VIII CONTENTS 2.4 PROBLEMS
43 3 THE ANALYTICAL MECHANICS OF LAGRANGE 47 3.1 LAGRANGIAN FORMALISM
AND THE LEAST ACTION PRINCIPLE 49 3.1.1 LEAST ACTION PRINCIPLE 49 3.1.2
LAGRANGE-EULER EQUATIONS 50 3.1.3 OPERATION OF THE OPTIMIZATION
PRINCIPLE 52 3.2 INVARIANCES AND CONSERVATION LAWS 53 3.2.1 CONJUGATE
MOMENTA AND GENERALIZED MOMENTA 53 3.2.2 CYCLIC VARIABLES 54 3.2.3
ENERGY AND TRANSLATIONS IN TIME 54 3.2.4 MOMENTUM AND TRANSLATIONS IN
SPACE 56 3.2.5 ANGULAR MOMENTUM AND ROTATIONS 57 3.2.6 DYNAMICAL
SYMMETRIES 57 3.3 VELOCITY-DEPENDENT FORCES 58 3.3.1 DISSIPATIVE SYSTEMS
58 3.3.2 LORENTZ FORCE 59 3.3.3 GAUGE INVARIANCE 60 3.3.4 MOMENTUM 61
3.4 LAGRANGIAN OF A RELATIVISTIC PARTICLE 61 3.4.1 FREE PARTICLE 61
3.4.2 ENERGY AND MOMENTUM 62 3.4.3 INTERACTION WITH AN ELECTROMAGNETIC
FIELD 63 3.5 PROBLEMS :. 65 4 HAMILTON'S CANONICAL FORMALISM 67 4.1
HAMILTON'S CANONICAL FORMALISM 68 4.1.1 CANONICAL EQUATIONS 69 4.2
DYNAMICAL SYSTEMS 70 4.2.1 POINCARE AND CHAOS IN THE SOLAR SYSTEM 71
4.2.2 THE BUTTERFLY EFFECT AND THE LORENZ ATTRACTOR 71 4.3 POISSON
BRACKETS AND PHASE SPACE 73 4.3.1 TIME EVOLUTION AND CONSTANTS OF THE
MOTION 74 4.3.2 CANONICAL TRANSFORMATIONS 75 4.3.3 PHASE SPACE;
LIOUVILLE'S THEOREM 78 4.3.4 ANALYTICAL MECHANICS AND QUANTUM MECHANICS
80 4.4 CHARGED PARTICLE IN AN ELECTROMAGNETIC FIELD 81 4.4.1 HAMILTONIAN
81 4.4.2 GAUGE INVARIANCE 82 4.5 THE ACTION AND THE HAMILTON-JACOBI
EQUATION 82 4.5.1 THE ACTION AS A FUNCTION OF THE COORDINATES AND TIME
83 4.5.2 THE HAMILTON-JACOBI EQUATION AND JACOBI THEOREM . 85 4.5.3
CONSERVATIVE SYSTEMS, THE REDUCED ACTION, AND THE MAUPERTUIS PRINCIPLE
87 4.6 ANALYTICAL MECHANICS AND OPTICS 89 CONTENTS IX 4.6.1 GEOMETRIC
LIMIT OF WAVE OPTICS 89 4.6.2 SEMICLASSICAL APPROXIMATION IN QUANTUM
MECHANICS . 91 4.7 PROBLEMS 92 LAGRANGIAN FIELD THEORY 97 5.1
VIBRATING STRING 98 5.2 FIELD EQUATIONS 99 5.2.1 GENERALIZED
LAGRANGE-EULER EQUATIONS 99 5.2.2 HAMILTONIAN FORMALISM 100 5.3 SCALAR
FIELD 101 5.4 ELECTROMAGNETIC FIELD 102 5.5 EQUATIONS OF FIRST ORDER IN
TIME 104 5.5.1 DIFFUSION EQUATION 104 5.5.2 SCHRODINGER EQUATION 104 5.6
PROBLEMS 105 MOTION IN A CURVED SPACE 107 6.1 CURVED SPACES 108 6.1.1
GENERALITIES 108 6.1.2 METRIC TENSOR 110 6.1.3 EXAMPLES ILL 6.2 FREE
MOTION IN A CURVED SPACE 112 6.2.1 LAGRANGIAN 113 6.2.2 EQUATIONS OF
MOTION 113 6.2.3 SIMPLE EXAMPLES 114 6.2.4 CONJUGATE MOMENTA AND THE
HAMILTONIAN 117 6.3 GEODESIC LINES 117 6.3.1 DEFINITION 117 6.3.2
EQUATION OF THE GEODESIES 118 6.3.3 EXAMPLES 119 6.3.4 MAUPERTUIS
PRINCIPLE AND GEODESIES 121 6.4 GRAVITATION AND THE CURVATURE OF
SPACE-TIME 122 6.4.1 NEWTONIAN GRAVITATION AND RELATIVITY 122 6.4.2 THE
SCHWARZSCHILD METRIC 124 6.4.3 GRAVITATION AND TIME FLOW 125 6.4.4
PRECESSION OF MERCURY'S PERIHELION 125 6.4.5 GRAVITATIONAL DEFLECTION OF
LIGHT RAYS 130 6.5 GRAVITATIONAL OPTICS AND MIRAGES _. 133 6.5.1
GRAVITATIONAL LENSING 133 6.5.2 GRAVITATIONAL MIRAGES 134 6.5.3 BARYONIC
DARK MATTER 139 6.6 PROBLEMS 144 X CONTENTS 7 FEYNMAN'S PRINCIPLE IN
QUANTUM MECHANICS 145 7.1 FEYNMAN'S PRINCIPLE 146 7.1.1 RECOLLECTIONS OF
ANALYTICAL MECHANICS 146 7.1.2 QUANTUM AMPLITUDES 147 7.1.3
SUPERPOSITION PRINCIPLE AND FEYNMAN'S PRINCIPLE 147 7.1.4 PATH INTEGRALS
148 7.1.5 AMPLITUDE OF SUCCESSIVE EVENTS 150 7.2 FREE PARTICLE 152 7.2.1
PROPAGATOR OF A FREE PARTICLE 152 7.2.2 EVOLUTION EQUATION OF THE FREE
PROPAGATOR 154 7.2.3 NORMALIZATION AND INTERPRETATION OF THE PROPAGATOR.
. . . 155 7.2.4 FOURIER AND SCHRODINGER EQUATIONS 155 7.2.5 ENERGY AND
MOMENTUM 156 7.2.6 INTERFERENCE AND DIFFRACTION 157 7.3 WAVE FUNCTION
AND THE SCHRODINGER EQUATION 157 7.3.1 FREE PARTICLE 158 7.3.2 PARTICLE
IN A POTENTIAL 159 7.4 CONCLUDING REMARKS 161 7.4.1 CLASSICAL LIMIT 161
7.4.2 ENERGY AND MOMENTUM 162 7.4.3 OPTICS AND ANALYTICAL MECHANICS 163
7.4.4 THE ESSENCE OF THE PHASE 163 7.5 PROBLEMS 164 SOLUTIONS 167
REFERENCES 179 INDEX 181 |
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| author | Basdevant, Jean-Louis 1939- |
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| author_facet | Basdevant, Jean-Louis 1939- |
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| author_sort | Basdevant, Jean-Louis 1939- |
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| callnumber-raw | QC174.17.V35 |
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| callnumber-sort | QC 3174.17 V35 |
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| classification_tum | PHY 013f |
| ctrlnum | (OCoLC)255454058 (DE-599)BVBBV023014629 |
| dewey-full | 531.01515 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 531 - Classical mechanics |
| dewey-raw | 531.01515 |
| dewey-search | 531.01515 |
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| dewey-tens | 530 - Physics |
| discipline | Physik |
| discipline_str_mv | Physik |
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| id | DE-604.BV023014629 |
| illustrated | Illustrated |
| index_date | 2024-07-02T19:10:47Z |
| indexdate | 2024-07-20T09:27:29Z |
| institution | BVB |
| isbn | 9780387377476 0387377476 0387377484 9780387377483 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016218806 |
| oclc_num | 255454058 |
| open_access_boolean | |
| owner | DE-703 DE-91G DE-BY-TUM DE-83 DE-706 |
| owner_facet | DE-703 DE-91G DE-BY-TUM DE-83 DE-706 |
| physical | X, 183 S. Ill., graph. Darst. |
| publishDate | 2007 |
| publishDateSearch | 2007 |
| publishDateSort | 2007 |
| publisher | Springer |
| record_format | marc |
| spelling | Basdevant, Jean-Louis 1939- Verfasser (DE-588)133559130 aut Variational principles in physics Jean-Louis Basdevant New York, NY Springer 2007 X, 183 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Field theory (Physics) Hamilton-Jacobi equations Lagrange equations Mechanics, Analytic Variational principles Physik (DE-588)4045956-1 gnd rswk-swf Variationsprinzip (DE-588)4062354-3 gnd rswk-swf Feldtheorie (DE-588)4016698-3 gnd rswk-swf Variationsprinzip (DE-588)4062354-3 s Feldtheorie (DE-588)4016698-3 s Physik (DE-588)4045956-1 s DE-604 text/html http://deposit.dnb.de/cgi-bin/dokserv?id=2839031&prov=M&dok_var=1&dok_ext=htm Inhaltstext HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016218806&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Basdevant, Jean-Louis 1939- Variational principles in physics Field theory (Physics) Hamilton-Jacobi equations Lagrange equations Mechanics, Analytic Variational principles Physik (DE-588)4045956-1 gnd Variationsprinzip (DE-588)4062354-3 gnd Feldtheorie (DE-588)4016698-3 gnd |
| subject_GND | (DE-588)4045956-1 (DE-588)4062354-3 (DE-588)4016698-3 |
| title | Variational principles in physics |
| title_auth | Variational principles in physics |
| title_exact_search | Variational principles in physics |
| title_exact_search_txtP | Variational principles in physics |
| title_full | Variational principles in physics Jean-Louis Basdevant |
| title_fullStr | Variational principles in physics Jean-Louis Basdevant |
| title_full_unstemmed | Variational principles in physics Jean-Louis Basdevant |
| title_short | Variational principles in physics |
| title_sort | variational principles in physics |
| topic | Field theory (Physics) Hamilton-Jacobi equations Lagrange equations Mechanics, Analytic Variational principles Physik (DE-588)4045956-1 gnd Variationsprinzip (DE-588)4062354-3 gnd Feldtheorie (DE-588)4016698-3 gnd |
| topic_facet | Field theory (Physics) Hamilton-Jacobi equations Lagrange equations Mechanics, Analytic Variational principles Physik Variationsprinzip Feldtheorie |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=2839031&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016218806&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT basdevantjeanlouis variationalprinciplesinphysics |