Mathematical Physics:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Weinheim
Wiley-VCH
2010
|
| Series: | Physics textbook
|
| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 435 - 437 |
| Physical Description: | XXII, 443 S. Ill. |
| ISBN: | 9783527408085 |
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MARC
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| 245 | 1 | 0 | |a Mathematical Physics |c Shigeji Fujita and Salvador V. Godoy |
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Record in the Search Index
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IMAGE 1
CONTENTS
PREFECE **
TABLE OF CONTENTS AND CATEGORIES XV
CONSTANTS, SIGNS, SYMBOLS, AND GENERAL REMARKS XVII
1 VECTORS 1
1.1 DEFINITION AND IMPORTANT PROPERTIES 1 1.1.1 DEFINITIONS 1 1.2
PRODUCT OF A SCALAR AND A VECTOR 2 1.3 POSITION VECTOR 2
1.4 SCALAR PRODUCT 3
1.5 VECTOR PRODUCT 4
1.6 DIFFERENTIATION 6
1.7 SPHERICAL COORDINATES 6 1.8 CYLINDRICAL COORDINATES 7
2 TENSORS AND MATRICES 21 2.1 DYADIC OR TENSOR PRODUCT 11 2.2 CARTESIAN
REPRESENTATION 12 2.3 DOT PRODUCT 13
2.3.1 UNIT TENSOR 14 2.4 SYMMETRIC TENSOR 15 2.5 EIGENVALUE PROBLEM 15
3 HAMILTONIAN MECHANICS 17 3.1 NEWTONIAN, LAGRANGIAN AND HAMILTONIAN
DESCRIPTIONS 17 3.1.1 NEWTONIAN DESCRIPTION 17 3.1.2 LAGRANGIAN
DESCRIPTION 19
3.1.3 HAMILTONIAN DESCRIPTION 20 3.2 STATE OF MOTION IN PHASE SPACE.
REVERSIBLE MOTION 22 3.3 HAMILTONIAN FOR A SYSTEM OF MANY PARTICLES 28
3.4 CANONICAL TRANSFORMATION 32 3.5 POISSON BRACKETS 36
BIBLIOGRAFISCHE INFORMATIONEN HTTP://D-NB.INFO/992134528
DIGITALISIERT DURCH
IMAGE 2
VI
4 COUPLED OSCILLATORS AND NORMAL MODES 43
4.1 OSCILLATIONS OF PARTICLES ON A STRING AND NORMAL MODES 43 4.2 NORMAL
COORDINATES 48
5 STRETCHED STRING 53 5.1 TRANSVERSE OSCILLATIONS OF A STRETCHED STRING
53 5.2 NORMAL COORDINATES FOR A STRING 58
6 VECTOR CALCULUS AND THE DEL OPERATOR 65 6.1 DIFFERENTIATION IN TIME 65
6.2 SPACE DERIVATIVES 66 6.2.1 THE GRADIENT 66
6.2.2 THE DIVERGENCE 67 6.2.3 THE CURL 67
6.2.4 SPACE DERIVATIVES OF PRODUCTS 67 6.3 SPACE DERIVATIVES IN
CURVILINEAR COORDINATES 69 6.3.1 SPHERICAL COORDINATES (R,6,(P) 69 6.3.2
CYLINDRICAL COORDINATES (P, P,Z) 69 6.4 INTEGRAL THEOREMS 70 6.4.1 THE
LINE INTEGRAL OF \* 70
6.4.2 STOKES'S THEOREM 70 6.5 GAUSS'S THEOREM 72 6.6 DERIVATION OF THE
GRADIENT, DIVERGENCE AND CURL 73
7 ELECTROMAGNETIC WAVES 77 7.1 ELECTRIC AND MAGNETIC FIELDS IN A VACUUM
77 7.2 THE ELECTROMAGNETIC FIELD THEORY 82
8 FLUID DYNAMICS 87
8.1 CONTINUITY EQUATION 87 8.2 FLUID EQUATION OF MOTION 89 8.3 FLUID
DYNAMICS AND STATISTICAL MECHANICS 92
9 IRREVERSIBLE PROCESSES 97 9.1 IRREVERSIBLE PHENOMENA, VISCOUS FLOW,
DIFFUSION 97 9.2 COLLISION RATE AND MEAN FREE PATH 100 9.3 OHM'S LAW,
CONDUCTIVITY, AND MATTHIESSEN'S RULE 103
10 THE ENTROPY 107 10.1 FOUNDATIONS OF THERMODYNAMICS 107 10.2 THE
CARNOT CYCLE 109 10.3 CARNOT'S THEOREM 111 10.4 HEAT ENGINES AND
REFRIGERATING MACHINES 113 10.5 CLAUSIUS'S THEOREM 114 10.6 THE ENTROPY
129 10.7 THE EXACT DIFFERENTIAL 222
IMAGE 3
VII
11 THERMODYNAMIC INEQUALITIES 225
11.1 IRREVERSIBLE PROCESSES AND THE ENTROPY 225 11.2 THE HEIMHOLTE FREE
ENERGY 128 11.3 THE GIBBS FREE ENERGY 230 11.4 MAXWELL RELATIONS 132
11.5 HEAT CAPACITIES 236 11.6 NONNEGATIVE HEAT CAPACITY AND
COMPRESSIBILITY 240
12 PROBABILITY, STATISTICS AND DENSITY 247 12.1 PROBABILITIES 247 12.2
BINOMIAL DISTRIBUTION 250 12.3 AVERAGE AND ROOT-MEAN-SQUARE DEVIATION.
RANDOM WALKS 253 12.4 MICROSCOPIC NUMBER DENSITY 256
12.5 DIRAC'S DELTA FUNCTION 260 12.6 THE THREE-DIMENSIONAL DELTA
FUNCTION 262
13 LIOUVILLE EQUATION 265 13.1 LIOUVILLE'S THEOREM 265 13.2 PROBABILITY
DISTRIBUTION FUNCTION. THE LIOUVILLE EQUATION 269 13.3 THE GIBBS
ENSEMBLE 173 13.4 MANY PARTICLES MOVING IN THREE DIMENSIONS 275 13.5
MORE ABOUT THE LIOUVILLE EQUATION 277 13.6 SYMMETRIES OF HAMILTONIANS
AND STATIONARY STATES 279
14 GENERALIZED VECTORS AND LINEAR OPERATORS 283 14.1 GENERALIZED
VECTORS. MATRICES 183 14.2 LINEAR OPERATORS 188 14.3 THE EIGENVALUE
PROBLEM 192 14.4 ORTHOGONAL REPRESENTATION 196
15 QUANTUM MECHANICS FOR A PARTICLE 201 15.1 QUANTUM DESCRIPTION OF A
LINEAR MOTION 202 15.2 THE MOMENTUM EIGENVALUE PROBLEM 207 15.3 THE
ENERGY EIGENVALUE PROBLEM 222
16 FOURIER SERIES AND TRANSFORMS 223 16.1 FOURIER SERIES 223 16.2
FOURIER TRANSFORMS 224 16.3 BRA AND KET NOTATIONS 225 16.4 HEISENBERG'S
UNCERTAINTY PRINCIPLE 217
17 QUANTUM ANGULAR MOMENTUM 221 17.1 QUANTUM ANGULAR MOMENTUM 221 17.2
PROPERTIES OF ANGULAR MOMENTUM 224
18 SPIN ANGULAR MOMENTUM 229 18.1 THE SPIN ANGULAR MOMENTUM 229 18.2 THE
SPIN OF THE ELECTRON 231
IMAGE 4
VILI
18.3 THE MAGNETOGYRIC RATIO 234
18.3.1 A. FREE ELECTRON 235 18.3.2 B. FREE PROTON 236 18.3.3 C. FREE
NEUTRON 237 18.3.4 D. ATOMIC NUCLEI 237
18.3.5 E. ATOMS AND IONS 237
19 TIME-DEPENDENT PERTURBATION THEORY 239 19.1 PERTURBATION THEORY 1;
THE DIRAC PICTURE 239 19.2 SCATTERING PROBLEM; FERMI'S GOLDEN RULE 242
19.3 PERTURBATION THEORY 2. SECOND INTERMEDIATE PICTURE 245
20 LAPLACE TRANSFORMATION 249 20.1 LAPLACE TRANSFORMATION 249 20.2 THE
ELECTRIC CIRCUIT EQUATION 251 20.3 CONVOLUTION THEOREM 252
20.4 LINEAR OPERATOR ALGEBRAS 253
21 QUANTUM HARMONIC OSCILLATOR 255 21.1 ENERGY EIGENVALUES 255 21.2
QUANTUM HARMONIC OSCILLATOR 259
22 PERMUTATION GROUP 263 22.1 PERMUTATION GROUP 263 22.2 ODD AND EVEN
PERMUTATIONS 267
23 QUANTUM STATISTICS 273 23.1 CLASSICAL INDISTINGUISHABLE PARTICLES 273
23.2 QUANTUM-STATISTICAL POSTULATE. SYMMETRIC STATES FOR BOSONS 276
23.3 ANTISYMMETRIC STATES FOR FERMIONS. PAULI'S EXCLUSION PRINCIPLE 278
23.4 OCCUPATION-NUMBER REPRESENTATION 280
24 THE FREE-ELECTRON MODEL 283 24.1 FREE ELECTRONS AND THE FERMI ENERGY
283 24.2 DENSITY OF STATES 287 24.3 QUALITATIVE DISCUSSION 291 24.4
SOMMERFELD'S CALCULATIONS 293
25 THE BOSE-EINSTEIN CONDENSATION 297 25.1 LIQUID HELIUM 297
25.2 THE BOSE-EINSTEIN CONDENSATION OF FREE BOSONS 298 25.3 BOSONS IN
CONDENSED PHASE 301
26 MAGNETIC SUSCEPTIBILITY 307 26.1 INTRODUCTION 307 26.2 PAULI
PARAMAGNETISM 308 26.3 MOTION OF A CHARGED PARTICLE IN ELECTROMAGNETIC
FIELDS 310 26.4 ELECTROMAGNETIC POTENTIALS 313 26.5 THE LANDAU STATES
AND ENERGIES 316
IMAGE 5
IX
26.6 THE DEGENERACY OF THE LANDAU LEVELS 317
26.7 LANDAU DIAMAGNETISM 321
27 THEORY OF VARIATIONS 329 27.,1 THE EULER-LAGRANGE EQUATION 329 27.2
FERMAT'S PRINCIPLE 331
27.3 HAMILTON'S PRINCIPLE 333 27.4 LAGRANGE'S FIELD EQUATION 333
28 SECOND QUANTIZATION 335 28.1 BOSON CREATION AND ANNIHILATION
OPERATORS 335 28.2 OBSERVABLES 338
28.3 FERMIONS CREATION AND ANNIHILATION OPERATORS 340 28.4 HEISENBERG
EQUATION OF MOTION 342
29 QUANTUM STATISTICS OF COMPOSITES 345 29.1
EHRENFEST-OPPENHEIMER-BETHE'S RULE 345 29.2 TWO-PARTIDE COMPOSITES 346
29.3 DISCUSSION 351
30 SUPERCONDUCTIVITY 357 30.1 BASIC PROPERTIES OF A SUPERCONDUCTOR 357
30.1.1 ZERO RESISTANCE 357 30.1.2 MEISSNER EFFECT 357
30.1.3 RING SUPERCURRENT AND FLUX QUANTIZATION 359 30.1.4 JOSEPHSON
EFFECTS 360 30.1.5 ENERGY GAP 362 30.1.6 SHARP PHASE CHANGE 363 30.2
OCCURRENCE OF A SUPERCONDUCTOR 363 30.2.1 ELEMENTAL SUPERCONDUCTORS 363
30.2.2 COMPOUND SUPERCONDUCTORS 363 30.2.3 HIGH-** SUPERCONDUCTORS 365
30.3 THEORETICAL SURVEY 365 30.3.1 THE CAUSE OF SUPERCONDUCTIVITY 365
30.3.2 THE BARDEEN-COOPER-SCHRIEFFER THEORY 366 30.4 QUANTUM-STATISTICAL
THEORY 367 30.4.1 THE FULL HAMILTONIAN 367 30.4.2 SUMMARY OF THE RESULTS
369
31 COMPLEX NUMBERS AND TAYLOR SERIES 375 31.1 COMPLEX NUMBERS 375 31.2
EXPONENTIAL AND LOGARITHMIC FUNCTIONS 377 31.2.1 LAWS OF EXPONENTS 377
31.2.2 NATURAL LOGARITHM 377
31.2.3 RELATIONSHIP BETWEEN EXPONENTIAL AND TRIGONOMETRIC FUNCTIONS 377
31.3 HYPERBOLIC FUNCTIONS 378 31.3.1 DEFINITION OF HYPERBOLIC FUNCTIONS
378
IMAGE 6
31.3.2 ADDITION FORMULAS 378
31.3.3 DOUBLE-ANGLE FORMULAS 379 31.3.4 SUM, DIFFERENCE AND PRODUCT OF
HYPERBOLIC FUNCTIONS 379 31.3.5 RELATIONSHIP BETWEEN HYPERBOLIC AND
TRIGONOMETRIC FUNCTIONS 379 31.4 TAYLOR SERIES 380
31.4.1 DERIVATIVES 380 31.4.2 TAYLOR SERIES 381 31.4.3 BINOMIAL SERIES
381 31.4.4 SERIES FOR EXPONENTIAL AND LOGARITHMIC FUNCTIONS 382
31.5 CONVERGENCE OF A SERIES 382
32 ANALYTICITY AND CAUCHY-RIEMANN EQUATIONS 385 32.1 THE ANALYTIC
FUNCTION 385 32.2 POLES 387
32.3 EXPONENTIAL FUNCTIONS 387 32.4 BRANCH POINTS 388 32.5 FUNCTION WITH
CONTINUOUS SINGULARITIES 389 32.6 CAUCHY-RIEMANN RELATIONS 390
32.7 CAUCHY-RIEMANN RELATIONS APPLICATIONS 391
33 CAUCHY'S FUNDAMENTAL THEOREM 395 33.1 CAUCHY'S FUNDAMENTAL THEOREM
395 33.2 LINE INTEGRALS 398
33.3 CIRCULAR INTEGRALS 400 33.4 CAUCHY'S INTEGRAL FORMULA 402
34 LAURENT SERIES 405 34.1 TAYLOR SERIES AND CONVERGENCE RADIUS 405 34.2
UNIFORM CONVERGENCE 406 34.3 LAURENT SERIES 407
35 MULTIVALUED FUNCTIONS 411 35.1 SQUARE-ROOT FUNCTIONS. RIEMANN SHEETS
AND CUT 411 35.2 MULTIVALUED FUNCTIONS 413
36 RESIDUE THEOREM AND ITS APPLICATIONS 415 36.1 RESIDUE THEOREM 415
36.2 INTEGRALS OF THE FORM /^ DX F(X) 417
36.3 INTEGRALS OF THE TYPE /^ DXE IX F(X) 419
36 A INTEGRALS OF THE TYPE F* D * /(COS * , SIN * ) 420 36.5
MISCELLANEOUS INTEGRALS 421
IMAGE 7
XI
APPENDIX A REPRESENTATION-INDEPENDENCE OF POISSON BRACKETS 423
APPENDIX * PROOF OF THE CONVOLUTION THEOREM 427
APPENDIXE STATISTICAL WEIGHT FOR THE LANDAU STATES 431
APPENDIX D USEFUL FORMULAS 433
REFERENCES 435
INDEX 439 |
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| id | DE-604.BV035839820 |
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| indexdate | 2024-07-20T10:24:05Z |
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| isbn | 9783527408085 |
| language | English |
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| physical | XXII, 443 S. Ill. |
| publishDate | 2010 |
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| spelling | Fujita, Shigeji Verfasser (DE-588)136795242 aut Mathematical Physics Shigeji Fujita and Salvador V. Godoy Weinheim Wiley-VCH 2010 XXII, 443 S. Ill. txt rdacontent n rdamedia nc rdacarrier Physics textbook Literaturverz. S. 435 - 437 Mathematische Physik Mathematical physics Mathematical physics Problems, exercises, etc Mathematische Physik (DE-588)4037952-8 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Mathematische Physik (DE-588)4037952-8 s DE-604 Godoy, Salvador Verfasser (DE-588)140148272 aut text/html http://deposit.dnb.de/cgi-bin/dokserv?id=3227426&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018698168&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Fujita, Shigeji Godoy, Salvador Mathematical Physics Mathematische Physik Mathematical physics Mathematical physics Problems, exercises, etc Mathematische Physik (DE-588)4037952-8 gnd |
| subject_GND | (DE-588)4037952-8 (DE-588)4123623-3 |
| title | Mathematical Physics |
| title_auth | Mathematical Physics |
| title_exact_search | Mathematical Physics |
| title_full | Mathematical Physics Shigeji Fujita and Salvador V. Godoy |
| title_fullStr | Mathematical Physics Shigeji Fujita and Salvador V. Godoy |
| title_full_unstemmed | Mathematical Physics Shigeji Fujita and Salvador V. Godoy |
| title_short | Mathematical Physics |
| title_sort | mathematical physics |
| topic | Mathematische Physik Mathematical physics Mathematical physics Problems, exercises, etc Mathematische Physik (DE-588)4037952-8 gnd |
| topic_facet | Mathematische Physik Mathematical physics Mathematical physics Problems, exercises, etc Lehrbuch |
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