Mathematical methods in chemistry and physics:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York u.a.
Plenum Press
1989
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | X, 651 S. graph. Darst. |
| ISBN: | 0306430665 |
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Record in the Search Index
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| adam_text | IMAGE 1
MATHEMATICAL METHODS
IN CHEMISTRY AND PHYSICS MICHAEL E. STARZAK STATE UNIVERSITY OF NEW YORK
AT BINGHAMTON BINGHAMTON, NEW YORK
PLENUM PRESS * NEW YORK AND LONDON
IMAGE 2
CONTENTS
1. VECTORS 1
1.1. VECTORS 1
1.2. VECTOR COMPONENTS 4
1.3. THE SCALAR PRODUCT 9
1.4. SCALAR PRODUCT APPLICATIONS 14
1.5. OTHER VECTOR COMBINATIONS 20
1.6. ORTHOGONALITY AND BIORTHOGONALITY 26
1.7. PROJECTION OPERATORS 32
1.8. LINEAR INDEPENDENCE AND DEPENDENCE 37
1.9. ORTHOGONALIZATION OF COORDINATES 40
1.10. VECTOR CALCULUS 46
PROBLEMS 52
2. FUNCTION SPACES 55
2.1. THE FUNCTION AS A VECTOR 55
2.2. FUNCTION SCALAR PRODUCTS AND ORTHOGONALITY 57
2.3. LINEAR INDEPENDENCE 63
2.4. ORTHOGONALIZATION OF BASIS FUNCTIONS 67
2.5. DIFFERENTIAL OPERATORS 70
2.6. GENERATION OF SPECIAL FUNCTIONS 77
2.7. FUNCTION RESOLUTION IN A SET OF BASIS FUNCTIONS 83
2.8. FOURIER SERIES 90
PROBLEMS 98
3. MATRICES 101
3.1. VECTOR ROTATIONS 101
3.2. SPECIAL MATRICES 109
3.3. MATRIX EQUATIONS AND INVERSES 114
3.4. DETERMINANTS 119
3.5. ROTATION OF COORDINATE SYSTEMS 125
3.6. PRINCIPAL AXES 133
3.7. EIGENVALUES AND THE CHARACTERISTIC POLYNOMIAL 140
VII
IMAGE 3
VIII CONTENTS
3.8. EIGENVECTORS 145
3.9. PROPERTIES OF THE CHARACTERISTIC POLYNOMIAL 152
3.10. ALTERNATE TECHNIQUES FOR EIGENVALUE AND EIGENVECTOR DETERMINATION
157
PROBLEMS 161
4. SIMILARITY TRANSFORMS AND PROJECTIONS 165
4.1. THE SIMILARITY TRANSFORM 165
4.2. SIMULTANEOUS DIAGONALIZATION 171
4.3. GENERALIZED CHARACTERISTIC EQUATIONS 176
4.4. MATRIX DECOMPOSITION USING EIGENVECTORS 181
4.5. THE LAGRANGE-SYLVESTER FORMULA 186
4.6. DEGENERATE EIGENVALUES 191
4.7. MATRIX FUNCTIONS AND EQUATIONS 199
4.8. DIAGONALIZATION OF TRIDIAGONAL MATRICES 205
4.9. OTHER TRIDIAGONAL MATRICES 211
4.10. ASYMMETRIE TRIDIAGONAL MATRICES 216
PROBLEMS 221
5. VIBRATIONS AND NORMAL MODES 225
5.1. NORMAL MODES 225
5.2. EQUATIONS OF MOTION FOR A DIATOMIC MOLECULE 232
5.3. NORMAL MODES FOR NON TRANSLATING SYSTEMS 240
5.4. NORMAL MODES USING PROJECTION OPERATORS 246
5.5. NORMAL MODES FOR HETEROATOMIC SYSTEMS 252
5.6. A HOMOGENEOUS ONE-DIMENSIONAL CRYSTAL 258
5.7. CYCLIC BOUNDARY CONDITIONS 264
5.8. HETEROATOMIC LINEAR CRYSTALS 271
5.9. NORMAL MODES FOR MOLECULES IN TWO DIMENSIONS 276
PROBLEMS 286
6. KINETICS 289
6.1. ISOMERIZATION REACTIONS 289
6.2. PROPERTIES OF MATRIX SOLUTIONS OF KINETIC EQUATIONS 294
6.3. KINETICS WITH DEGENERATE EIGENVALUES 300
6.4. THE MASTER EQUATION 309
6.5. SYMMETRIZATION OF THE MASTER EQUATION 315
6.6. THE WEGSCHEIDER CONDITIONS AND CYCLIC REACTIONS 321
6.7. GRAPH THEORY IN KINETICS 332
6.8. GRAPHS FOR KINETICS 337
6.9. MEAN FIRST PASSAGE TIMES 340
6.10. EVALUATION OF MEAN FIRST PASSAGE TIMES 346
6.11. STEPLADDER MODELS 351
PROBLEMS 356
IMAGE 4
CONTENTS IX
7. STATISTICAL MECHANICS 359
7.1. THE WIND-TREE MODEL 359
7.2. STATISTICAL MECHANICS OF LINEAR POLYMERS 366
7.3. POLYMERS WITH NEAREST-NEIGHBOR INTERACTIONS 373
7.4. OTHER ONE-DIMENSIONAL SYSTEMS 379
7.5. TWO-DIMENSIONAL SYSTEMS 385
7.6. NON-NEAREST-NEIGHBOR INTERACTIONS 389
7.7. REDUCTION OF MATRIX ORDER 393
7.8. THE KINETIC ISING MODEL 399
PROBLEMS 407
8. QUANTUM MECHANICS 409
8.1. HYBRID ATOMIC ORBITALS 409
8.2. MATRIX QUANTUM MECHANICS 415
8.3. HUECKEL MOLECULAR ORBITALS FOR LINEAR MOLECULES 421
8.4. HUECKEL THEORY FOR CYCLIC MOLECULES 430
8.5. DEGENERATE MOLECULAR ORBITALS FOR CYCLIC MOLECULES 437
8.6. THE PAULI SPIN MATRICES 444
8.7. LOWERING AND RAISING OPERATORS 452
8.8. PROJECTION OPERATORS 461
PROBLEMS 467
9. DRIVEN SYSTEMS AND FLUCTUATIONS 469
9.1. SINGLET-SINGLET KINETICS 469
9.2. MULTILEVEL DRIVEN PHOTOCHEMICAL SYSTEMS 475
9.3. LASER SYSTEMS 482
9.4. IONIC CHANNELS 487
9.5. EQUILIBRIUM AND STATIONARY-STATE PROPERTIES 493
9.6. FLUCTUATIONS ABOUT EQUILIBRIUM 500
9.7. FLUCTUATIONS DURING REACTIONS 509
9.8. THE KINETICS OF SINGLE CHANNELS IN MEMBRANES 517
PROBLEMS 524
10. OTHER TECHNIQUES: PERTURBATION THEORY AND DIRECT PRODUCTS 527
10.1. DEVELOPMENT OF PERTURBATION THEORY 527
10.2. FIRST-ORDER PERTURBATION THEORY-EIGENVALUES 532
10.3. FIRST-ORDER PERTURBATION THEORY-EIGENVECTORS 539
10.4. SECOND-ORDER PERTURBATION THEORY-EIGENVALUES 546
10.5. SECOND-ORDER PERTURBATION THEORY-EIGENVECTORS 550
10.6. DIRECT SUMS AND PRODUCTS 557
10.7. A TWO-DIMENSIONAL COUPLED OSCILLATOR SYSTEM 564
PROBLEMS 571
11. INTRODUCTION TO GROUP THEORY 573
11.1. VECTORS AND SYMMETRY OPERATIONS 573
IMAGE 5
X CONTENTS
11.2. MATRIX REPRESENTATIONS OF SYMMETRY OPERATIONS 579
11.3. GROUP OPERATIONS AND TABLES 586
11.4. PROPERTIES OF IRREDUCIBLE REPRESENTATIONS 594
11.5. APPLICATIONS OF GROUP THEORY 602
11.6. GENERATION OF MOLECULAR ORBITALS 608
11.7. NORMAL VIBRATIONAL MODES 615
11.8. LIGAND FIELD THEORY 625
11.9. DIRECT PRODUCTS OF GROUP ELEMENTS 632
11.10. DIRECT PRODUCTS AND INTEGRALS 640
PROBLEMS 645
INDEX 647
|
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| author | Starzak, Michael E. |
| author_facet | Starzak, Michael E. |
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| dewey-search | 510/.2454 |
| dewey-sort | 3510 42454 |
| dewey-tens | 510 - Mathematics |
| discipline | Chemie / Pharmazie Mathematik |
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| indexdate | 2024-07-09T16:03:27Z |
| institution | BVB |
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| language | English |
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| spelling | Starzak, Michael E. Verfasser aut Mathematical methods in chemistry and physics New York u.a. Plenum Press 1989 X, 651 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Chimie Chimie - Mathématiques Chimie - Mathématiques ram Méthode mathématique Physique Physique mathématique Physique mathématique ram Chemie Mathematik Chemistry Mathematics Physics Mathematics Mathematik (DE-588)4037944-9 gnd rswk-swf Physik (DE-588)4045956-1 gnd rswk-swf Chemie (DE-588)4009816-3 gnd rswk-swf Mathematik (DE-588)4037944-9 s Physik (DE-588)4045956-1 s DE-604 Chemie (DE-588)4009816-3 s GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002330263&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Starzak, Michael E. Mathematical methods in chemistry and physics Chimie Chimie - Mathématiques Chimie - Mathématiques ram Méthode mathématique Physique Physique mathématique Physique mathématique ram Chemie Mathematik Chemistry Mathematics Physics Mathematics Mathematik (DE-588)4037944-9 gnd Physik (DE-588)4045956-1 gnd Chemie (DE-588)4009816-3 gnd |
| subject_GND | (DE-588)4037944-9 (DE-588)4045956-1 (DE-588)4009816-3 |
| title | Mathematical methods in chemistry and physics |
| title_auth | Mathematical methods in chemistry and physics |
| title_exact_search | Mathematical methods in chemistry and physics |
| title_full | Mathematical methods in chemistry and physics |
| title_fullStr | Mathematical methods in chemistry and physics |
| title_full_unstemmed | Mathematical methods in chemistry and physics |
| title_short | Mathematical methods in chemistry and physics |
| title_sort | mathematical methods in chemistry and physics |
| topic | Chimie Chimie - Mathématiques Chimie - Mathématiques ram Méthode mathématique Physique Physique mathématique Physique mathématique ram Chemie Mathematik Chemistry Mathematics Physics Mathematics Mathematik (DE-588)4037944-9 gnd Physik (DE-588)4045956-1 gnd Chemie (DE-588)4009816-3 gnd |
| topic_facet | Chimie Chimie - Mathématiques Méthode mathématique Physique Physique mathématique Chemie Mathematik Chemistry Mathematics Physics Mathematics Physik |
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