Mathematica for theoretical physics: 2 Electrodynamics, quantum mechanics, general relativity and fractals
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Springer
2005
|
| Ausgabe: | 2. ed., expanded, and updated version of the orig. German version |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XVI, S. 546 - 942 Ill., graph. Darst. 1 CD-ROM (12 cm) |
| ISBN: | 0387251138 9780387219332 |
Internformat
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Datensatz im Suchindex
| _version_ | 1804139082671980544 |
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| adam_text | MATHEMATICA FOR THEORETICAL PHYSICS ELECTRODYNAMICS, QUANTUM MECHANICS,
GENERAL RELATIVITY, AND FRACTALS SECOND EDITION GERD BAUMANN CD-ROM
INCLUDED 4Y SPRINGER CONTENTS CLASSICAL MECHANICS AND NONLINEAR DYNAMICS
PREFACE INTRODUCTION 1.1 BASICS 1. 1. 1. 1. 1. 1. L.L 1.2 1.3 1.4 1.5
1.6 STRUCTURE OF MATHEMATICA INTERACTIVE USE OF MATHEMATICA SYMBOLIC
CALCULATIONS NUMERICAL CALCULATIONS GRAPHICS PROGRAMMING CLASSICAL
MECHANICS 2.1 INTRODUCTION 2.2 MATHEMATICAL TOOLS 2.2.1 2.2.2 2.2.3
2.2.4 2.2.5 2.2.6 2.2.7 2.2.8 2.2.9 2. 2.10 INTRODUCTION COORDINATES
COORDINATE TRANSFORMATIONS AND MATRICES SCALARS VECTORS TENSORS VECTOR
PRODUCTS DERIVATIVES INTEGRALS EXERCISES VLL 1 1 2 4 6 11 13 23 31 31 35
35 36 38 54 57 59 64 69 73 74 XII CONTENTS 2.3 2.4 2.5 2.6 2.7
KINEMATICS 2.3.1 INTRODUCTION 2.3.2 VELOCITY 2.3.3 ACCELERATION 2.3.4
KINEMATIC EXAMPLES 2.3.5 EXERCISES NEWTONIAN MECHANICS 2.4.1
INTRODUCTION 2.4.2 FRAME OF REFERENCE 2.4.3 TIME 2.4.4 MASS 2.4.5
NEWTON S LAWS 2.4.6 FORCES IN NATURE 2.4.7 CONSERVATION LAWS 2.4.8
APPLICATION OF NEWTON S SECOND LAW 2.4.9 EXERCISES 2.4.10 PACKAGES AND
PROGRAMS CENTRAL FORCES 2.5.1 INTRODUCTION 2.5.2 KEPLER S LAWS 2.5.3
CENTRAL FIELD MOTION 2.5.4 TWO-PARTICLE COLLISONS AND SCATTERING 2.5.5
EXERCISES 2.5.6 PACKAGES AND PROGRAMS CALCULUS OF VARIATIONS 2.6.1
INTRODUCTION 2.6.2 THE PROBLEM OF VARIATIONS 2.6.3 EULER S EQUATION
2.6.4 EULER OPERATOR 2.6.5 ALGORITHM USED IN THE CALCULUS OF VARIATIONS
2.6.6 EULER OPERATOR FOR Q DEPENDENT VARIABLES 2.6.7 EULER OPERATOR
FORQ+P DIMENSIONS 2.6.8 VARIATIONS WITH CONSTRAINTS 2.6.9 EXERCISES
2.6.10 PACKAGES AND PROGRAMS LAGRANGE DYNAMICS 2.7.1 INTRODUCTION 2.7.2
HAMILTON S PRINCIDLE HISTORICAL REMARKS 76 76 77 81 82 94 96 96 98 100
101 103 106 111 118 188 188 201 201 202 208 240 272 273 274 274 276 281
283 284 293 2% 300 303 303 305 305 306 CONTENTS XIII 2.7.3 HAMILTON S
PRINCIPLE 313 2.7.4 SYMMETRIES AND CONSERVATION LAWS 341 2.7.5 EXERCISES
351 2.7.6 PACKAGES AND PROGRAMS 351 2.8 HAMILTONIAN DYNAMICS 354 2.8.1
INTRODUCTION 354 2.8.2 LEGENDRE TRANSFORM 355 2.8.3 HAMILTON S EQUATION
OF MOTION 362 2.8.4 HAMILTON S EQUATIONS AND THE CALCULUS OF VARIATION
366 2.8.5 LIOUVILLE S THEOREM 373 2.8.6 POISSON BRACKETS 377 2.8.7
MANIFOLDS AND CLASSES 384 2.8.8 CANONICAL TRANSFORMATIONS 396 2.8.9
GENERATING FUNCTIONS 398 2.8.10 ACTION VARIABLES 403 2.8.11 EXERCISES
419 2.8.12 PACKAGES AND PROGRAMS 419 2.9 CHAOTIC SYSTEMS 422 2.9.1
INTRODUCTION 422 2.9.2 DISCRETE MAPPINGS AND HAMILTONIANS 431 2.9.3
LYAPUNOV EXPONENTS 435 2.9.4 EXERCISES 448 2.10 RIGID BODY 449 2.10.1
INTRODUCTION 449 2.10.2 THE INERTIA TENSOR 450 2.10.3 THE ANGULAR
MOMENTUM 453 2.10.4 PRINCIPAL AXES OF INERTIA 454 2.10.5 STEINER S
THEOREM 460 2.10.6 EULER S EQUATIONS OF MOTION 462 2.10.7 FORCE-FREE
MOTION OF A SYMMETRICAL TOP 467 2.10.8 MOTION OF A SYMMETRICAL TOP IN A
FORCE FIELD 471 2.10.9 EXERCISES 481 2.10.10 PACKAGES AND PROGRAMMS 481
3 NONLINEAR DYNAMICS 485 3.1 INTRODUCTION 485 3.2 THE KORTEWEG-DE VRIES
EQUATION 488 3.3 SOLUTION OF THE KORTEWEG-DE VRIES EQUATION 492 XIV
CONTENTS 3.3.1 THE INVERSE SCATTERING TRANSFORM 492 3.3.2 SOLITON
SOLUTIONS OF THE KORTEWEG-DE VRIES EQUATION 498 3.4 CONSERVATION LAWS OF
THE KORTEWEG-DE VRIES EQUATION 505 3.4.1 DEFINITION OF CONSERVATION LAWS
506 3.4.2 DERIVATION OF CONSERVATION LAWS 508 3.5 NUMERICAL SOLUTION OF
THE KORTEWEG-DE VRIES EQUATION 511 3.6 EXERCISES 515 3.7 PACKAGES AND
PROGRAMS 516 3.7.1 SOLUTION OF THE KDV EQUATION 516 3.7.2 CONSERVATION
LAWS FOR THE KDV EQUATION 517 3.7.3 NUMERICAL SOLUTION OF THE KDV
EQUATION 518 REFERENCES 521 INDEX 529 ELECTRODYNAMICS, QUANTUM
MECHANICS, GENERAL RELATIVITY, AND FRACTALS PREFACE ELECTRODYNAMICS 4.1
4.2 4.3 4.4 4.5 4.6 INTRODUCTION POTENTIAL AND ELECTRIC FIELD OF
DISCRETE CHARGE DISTRIBUTIONS BOUNDARY PROBLEM OF ELECTROSTATICS TWO
IONS IN THE PENNING TRAP 4.4.1 THE CENTER OF MASS MOTION 4.4.2 RELATIVE
MOTION OF THE IONS EXERCISES PACKAGES AND PROGRAMS 4.6.1 POINT CHARGES
4.6.2 BOUNDARY PROBLEM 4.6.3 PENNING TRAP QUANTUM MECHANICS 5.1 5.2
INTRODUCTION THE SCHRODINEER EAUATION VLL 545 545 548 555 566 569 572
577 578 578 581 582 587 587 590 CONTENTS XV 5.3 ONE-DIMENSIONAL
POTENTIAL 595 5.4 THE HARMONIC OSCILLATOR 609 5.5 ANHARMONIC OSCILLATOR
619 5.6 MOTION IN THE CENTRAL FORCE FIELD 631 5.7 SECOND VIRIAL
COEFFICIENT AND ITS QUANTUM CORRECTIONS 642 5.7.1 THE SVC AND ITS
RELATION TO THERMODYNAMIC PROPERTIES 644 5.7.2 CALCULATION OF THE
CLASSICAL SVC B C (T) FOR THE (2 N - N) -POTENTIAL 646 5.7.3 QUANTUM
MECHANICAL CORRECTIONS B QI (T) AND S, 2 (R)OFTHESVC 655 5.7.4 SHAPE
DEPENDENCE OF THE BOYLE TEMPERATURE 680 5.7.5 THE HIGH-TEMPERATURE
PARTITION FUNCTION FOR DIATOMIC MOLECULES 684 5.8 EXERCISES 687 5.9
PACKAGES AND PROGRAMS 688 5.9.1 QUANTUMWELL 688 5.9.2 HARMONICOSCILLATOR
693 5.9.3 ANHARMONICOSCILLATOR 695 5.9.4 CENTRALFIELD 698 6 GENERAL
RELATIVITY 703 6.1 INTRODUCTION 703 6.2 THE ORBITS IN GENERAL RELATIVITY
707 6.2.1 QUASIELLIPTIC ORBITS 713 6.2.2 ASYMPTOTIC CIRCLES 719 6.3
LIGHT BENDING IN THE GRAVITATIONAL FIELD 720 6.4 EINSTEIN S FIELD
EQUATIONS (VACUUM CASE) 725 6.4.1 EXAMPLES FOR METRIC TENSORS 727 6.4.2
THE CHRISTOFFEL SYMBOLS 731 6.4.3 THE RIEMANN TENSOR 731 6.4.4
EINSTEIN S FIELD EQUATIONS 733 6.4.5 THE CARTESIAN SPACE 734 6.4.6
CARTESIAN SPACE IN CYLINDRICAL COORDINATES 736 6.4.7 EUCLIDEAN SPACE IN
POLAR COORDINATES 737 6.5 THE SCHWARZSCHILD SOLUTION 739 6.5.1 THE
SCHWARZSCHILD METRIC IN EDDINGTON-FINKELSTEIN FORM 739 XVI CONTENTS 6.6
6.7 6.8 6.5.2 DINGLE S METNC 6.5.3 SCHWARZSCHILD METRIC IN KRUSKAL
COORDINATES THE REISSNER-NORDSTROM SOLUTION FOR A CHARGED MASS POINT
EXERCISES PACKAGES AND PROGRAMS 6.8.1 EULERLAGRANGE EQUATIONS 6.8.2
PERIHELIONSHIFT 6.8.3 LIGHTBENDING 7 FRACTALS 7.1 7.2 7.3 7.4 7.5 7.6
7.7 7.8 INTRODUCTION MEASURING A BORDERLINE 7.2.1 BOX COUNTING THE KOCH
CURVE MULTI FRACTALS 7.4.1 MULTIFRACTALS WITH COMMON SCALING FACTOR THE
RENORMLIZATION GROUP FRACTIONAL CALCULUS 7.6.1 HISTORICAL REMARKS ON
FRACTIONAL CALCULUS 7.6.2 THE RIEMANN-LIOUVILLE CALCULUS 7.6.3 MELLIN
TRANSFORMS 7.6.4 FRACTIONAL DIFFERENTIAL EQUATIONS EXERCISES PACKAGES
AND PROGRAMS 7.8.1 TREE GENERATION 7.8.2 KOCH CURVES 7.8.3 MULTIFACTALS
7.8.4 RENORMALIZATION 7.8.5 FRACTIONAL CALCULUS APPENDIX A.I A.2 A.3
PROGRAM INSTALLATION GLOSSARY OF FILES AND FUNCTIONS MATHEMATICA
FUNCTIONS REFERENCES INDEX 742 748 752 759 761 761 762 767 773 773 776
781 790 795 798 801 809 810 813 830 856 883 883 883 886 892 895 897 899
899 900 910 923 931
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| id | DE-604.BV023865132 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T21:38:26Z |
| institution | BVB |
| isbn | 0387251138 9780387219332 |
| language | English |
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| physical | XVI, S. 546 - 942 Ill., graph. Darst. 1 CD-ROM (12 cm) |
| publishDate | 2005 |
| publishDateSearch | 2005 |
| publishDateSort | 2005 |
| publisher | Springer |
| record_format | marc |
| spelling | Baumann, Gerd 1956- Verfasser (DE-588)142960241 aut Mathematica for theoretical physics 2 Electrodynamics, quantum mechanics, general relativity and fractals Gerd Baumann 2. ed., expanded, and updated version of the orig. German version New York [u.a.] Springer 2005 XVI, S. 546 - 942 Ill., graph. Darst. 1 CD-ROM (12 cm) txt rdacontent n rdamedia nc rdacarrier (DE-604)BV023818776 2 HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017528979&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Baumann, Gerd 1956- Mathematica for theoretical physics |
| title | Mathematica for theoretical physics |
| title_auth | Mathematica for theoretical physics |
| title_exact_search | Mathematica for theoretical physics |
| title_full | Mathematica for theoretical physics 2 Electrodynamics, quantum mechanics, general relativity and fractals Gerd Baumann |
| title_fullStr | Mathematica for theoretical physics 2 Electrodynamics, quantum mechanics, general relativity and fractals Gerd Baumann |
| title_full_unstemmed | Mathematica for theoretical physics 2 Electrodynamics, quantum mechanics, general relativity and fractals Gerd Baumann |
| title_short | Mathematica for theoretical physics |
| title_sort | mathematica for theoretical physics electrodynamics quantum mechanics general relativity and fractals |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017528979&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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