Topics in quantum mechanics:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boston ; Basel ; Berlin
Birkhäuser
2003
|
| Schriftenreihe: | Progress in mathematical physics
27 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XV, 396 S. |
| ISBN: | 0817643117 3764343117 |
Internformat
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Datensatz im Suchindex
| _version_ | 1804129650720374784 |
|---|---|
| adam_text | FLOYD WILLIAMS TOPICS IN QUANTUM MECHANICS BIRKHAUSER BOSTON * BASEL *
BERLIN CONTENTS PREFACE XIII ACKNOWLEDGMENTS XV I INTRODUCTORY CONCEPTS
IN QUANTUM THEORY 1 0 UNITS OF MEASUREMENT 3 1 QUANTUM MECHANICS: SOME
REMARKS AND THEMES 7 1.1 PLANCK QUANTIZATION 7 1.2 THE BOHR FREQUENCY
RULE AND EMISSION SPECTRA 9 1.3 SCHRODINGER S EQUATION 14 1.4 THE DE
BROGLIE WAVELENGTH 17 1.5 HEISENBERG S UNCERTAINTY PRINCIPLE 20 1.6
BOHR S COMPLEMENTARITY PRINCIPLE 22 2 EQUATIONS OF MOTION IN CLASSICAL
MECHANICS 25 2.1 INTRODUCTION 25 2.2 MOTION IN ONE DIMENSION 26 2.3
MOTION IN THREE DIMENSIONS 31 2.4 MANY PARTICLES IN THREE DIMENSIONS 32
2.5 COULOMB AND GRAVITATIONAL POTENTIALS 34 2.6 HAMILTON S EQUATIONS OF
MOTION 36 2.7 LAGRANGE S EQUATIONS OF MOTION 40 2.8 CENTER OF MASS
COORDINATES 44 VIII CONTENTS QUANTIZATION AND THE SCHRODINGER EQUATION
51 3.1 THE ONE-DIMENSIONAL SCHRODINGER EQUATION 51 3.2 THE QUANTIZED
HARMONIC OSCILLATOR 53 3.3 A FINITE POTENTIAL WELL 53 3.4 SCHRODINGER S
EQUATION FOR A SYSTEM 58 3.5 SCHRODINGER S EQUATION FOR AN ATOM 60 3.6
NON-QUANTIZATION OF THE FREE PARTICLE 63 3.7 QUANTIZATION, LARGE
EIGENVALUES, AND SPECTRAL ZETA FUNCTIONS . . 65 3.8 THE DIFFEOMORPHISM
3 AGAIN 72 3.9 SOME BRIEF REMARKS ON AXIOMS 77 HYPERGEOMETRIC EQUATIONS
AND SPECIAL FUNCTIONS 81 4.1 INITIAL REMARKS 81 4.2 DIFFERENTIAL
EQUATIONS OF HYPERGEOMETRIC TYPE 82 4.3 REDUCTION TO CANONICAL FORM 83
4.4 SOLUTIONS OF AY + RY + AY - 0 87 4.5 EXAMPLES OF THE REDUCTION
TECHNIQUE 91 4.6 EXAMPLES: HERMITE, LEGENDRE, LAGUERRE, JACOBI 95 4.7
ORTHOGONALITY 98 4.8 NORMALIZED WAVE FUNCTIONS FOR THE HARMONIC
OSCILLATOR 109 4.9 FURTHER EXAMPLES OF THE REDUCTION TECHNIQUE: THE
POSCHL-TELLER POTENTIAL 110 APPENDIX 4A: SPHERICAL HARMONICS 115
APPENDIX 4B: THE POLYNOMIALS L N 121 HYDROGEN-LIKE ATOMS 123 5.1
SOLUTIONS OF SCHRODINGER S EQUATION FOR HYDROGENIC ATOMS . . . .124 5.2
NORMALIZED WAVE FUNCTIONS 130 5.3 THE WAVE FUNCTIONS Y/ N I M FOR SMALL
N 132 5.4 QUANTIZATION OF ANGULAR MOMENTUM 138 5.5 THE AVERAGE DISTANCE
OF THE ELECTRON FROM THE NUCLEUS 148 5.6 THE RITZ-RYDBERG FORMULA:
FURTHER EXAMPLES 150 5.7 WAVE FUNCTION ORTHOGONALITY 152 5.8 GROUND
STATE ENERGY OF HYDROGEN-LIKE ATOMS 154 APPENDIX 5A: COMMUTATION
RELATIONS FOR ANGULAR MOMENTUM OPERATORS 154 HEISENBERG S UNCERTAINTY
PRINCIPLE 157 6.1 HEISENBERG S INEQUALITY 157 6.2 HEISENBERG S
UNCERTAINTY PRINCIPLE 162 6.3 EXAMPLE 169 GROUP REPRESENTATIONS AND
SELECTION RULES 171 7.1 GROUP REPRESENTATIONS 171 7.2 CONTRAGREDIENT AND
TENSOR PRODUCT REPRESENTATIONS 178 7.3 SUBREPRESENTATIONS 181 CONTENTS
IX 7.4 GROUP ACTIONS 182 7.5 AN ABSTRACT SELECTION RULE 183 7.6 SOME
PRELIMINARY APPLICATIONS OF THEOREM 7.2 188 7.7 TIME-DEPENDENT
PERTURBATIONS AND SPECTROSCOPIC SELECTION RULES 190 7.8 SPECTROSCOPIC
SELECTION RULES FOR THE HYDROGENIC ATOM 201 7.9 A GENERAL QUANTUM
MECHANICAL SELECTION RULE 202 7.10 GROUP INVARIANCE OF SCHRODINGER S
EQUATION 203 7.11 THE REPRESENTATIONS 1* OF S N , AND THE IRREDUCIBLE
REPRESENTA- TIONS OF ^3 204 APPENDIX 7A: PROOF OF THEOREMS 7.2 AND 7.6
208 APPENDIX 7B: PROOF OF PROPOSITION 7.2 213 APPENDIX 7C: PROOF OF
EQUATION (7.1.10) 214 APPENDIX 7D: REMARKS ON EQUATION (7.7.54) 215 8
THE QUANTIZED HAMILTONIAN FOR A CHARGED PARTICLE IN AN ELECTROMAGNETIC
FIELD 217 8.1 THE MOTION OF A CHARGED PARTICLE IN AN ELECTROMAGNETIC
FIELD . . 217 8.2 CLASSICAL AND QUANTIZED HAMILTONIAN FOR A CHARGED
PARTICLE .... 223 APPENDIX 8A: THE ELECTRIC FIELD DUE TO A COLLECTION OF
POINT CHARGES, ELECTRIC POTENTIAL, AND VOLTAGE 225 APPENDIX 8B: ELECTRIC
DIPOLE MOMENTS 230 9 SPIN WAVE FUNCTIONS 233 9.1 SPIN OPERATORS 233 9.2
PAULI SPIN WAVE FUNCTIONS 236 9.3 THE ZEEMAN EFFECT FOR WEAK MAGNETIC
FIELDS 240 APPENDIX 9A: MAGNETIC DIPOLE MOMENTS 245 APPENDIX 9B:
QUANTIZATION OF THE MAGNETIC DIPOLE MOMENT /? 248 APPENDIX 9C:
CONSTRUCTION OF HIGHER SPIN OPERATORS 249 10 INTRODUCTION TO
MULTI-ELECTRON ATOMS 253 10.1 FIRST-ORDER CORRECTION TO E O 253 10.2
HELIUM-LIKE ATOMS: THEIR GROUND-STATE ENERGIES 256 10.3 PAULI S
EXCLUSION PRINCIPLE AND ELECTRON CONFIGURATIONS 260 APPENDIX 10A: ON THE
INTEGRAL IN (10.2.19) 267 11 SOME SELECTED TOPICS , 269 11 FRESNEL
INTEGRALS AND FEYNMAN INTEGRALS 271 11.1 FRESNEL INTEGRALS 271 11.2
FEYNMAN PATH INTEGRALS 280 APPENDIX 11 A: GAUSSIAN INTEGRALS 288 12 PATH
INTEGRAL FOR THE HARMONIC OSCILLATOR 291 13 EUCLIDEAN PATH INTEGRALS 299
13.1 EUCLIDEAN PATH INTEGRALS 299 X CONTENTS 13.2 WAVE FUNCTION
EXPANSION OF THE EUCLIDEAN PATH INTEGRAL 303 14 THE DENSITY MATRIX AND
PARTITION FUNCTION IN QUANTUM STATISTICAL MECHANICS 307 14.1 HELMHOLTZ
FREE ENERGY, ENTROPY AND INTERNAL ENERGY 307 14.2 A ZETA FUNCTION
REPRESENTATION OF THE FREE ENERGY 310 APPENDIX 14A: JACOBI INVERSION 314
15 ZETA REGULARIZATION 317 16 HELMHOLTZ FREE ENERGY FOR CERTAIN
NEGATIVELY CURVED SPACE-TIMES, AND THE SELBERG TRACE FORMULA 321 16.1 A
ZETA FUNCTION FOR KALUZA-KLEIN SPACE-TIMES MODELED ON SO (D, )/SO(D),
AND A TRACE FORMULA FOR COMPACT QUOTIENTS OF SCW, 1) 321 16.2
TEMPERATURE ASYMPTOTICS 331 17 THE ZETA FUNCTION OF A PRODUCT OF LAPLACE
OPERATORS AND THE MULTIPLICATIVE ANOMALY FOR X* 333 17.1 DETLIL 2 =DETL]
DETL 2 ? 333 17.2 EXPLICIT MEROMORPHIC STRUCTURE OF CR(S;/ I ^2) 335 18
SCHRODINGER S EQUATION AND GAUGE THEORY 341 PATRICK SHANAHAN 341 18.1 A
BRIEF INTRODUCTION TO GAUGE THEORY 341 18.2 343 18.3 346 18.4 349 18.5
352 ABOUT THE AUTHOR . 357 GENERAL APPENDICES 359 APPENDIX A: SOME
FURTHER ELECTRON CONFIGURATIONS 361 APPENDIX B: MENDELEEV PERIODIC TABLE
365 APPENDIX C: DETERMINANTS FOR STRING WORLD-SHEETS THAT ARE TORI:
ANOTHER EXAMPLE OF ZETA REGULARIZATION 369 APPENDIX D: EVALUATION OF THE
INTEGRAL I N = J RN J RN E L-P DXDY 373 APPENDIX E: SOME INFORMAL
COMMENTS ON QFT 379 REFERENCES 385 INDEX 393
|
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| indexdate | 2024-07-09T19:08:31Z |
| institution | BVB |
| isbn | 0817643117 3764343117 |
| language | English |
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| physical | XV, 396 S. |
| publishDate | 2003 |
| publishDateSearch | 2003 |
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| publisher | Birkhäuser |
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| series | Progress in mathematical physics |
| series2 | Progress in mathematical physics |
| spelling | Williams, Floyd L. 1939- Verfasser (DE-588)107924005 aut Topics in quantum mechanics Floyd Williams Boston ; Basel ; Berlin Birkhäuser 2003 XV, 396 S. txt rdacontent n rdamedia nc rdacarrier Progress in mathematical physics 27 Mathematische Physik Quantentheorie Mathematical physics Quantum theory Quantenmechanik (DE-588)4047989-4 gnd rswk-swf Quantenmechanik (DE-588)4047989-4 s DE-604 Progress in mathematical physics 27 (DE-604)BV013823265 27 HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010070311&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Williams, Floyd L. 1939- Topics in quantum mechanics Progress in mathematical physics Mathematische Physik Quantentheorie Mathematical physics Quantum theory Quantenmechanik (DE-588)4047989-4 gnd |
| subject_GND | (DE-588)4047989-4 |
| title | Topics in quantum mechanics |
| title_auth | Topics in quantum mechanics |
| title_exact_search | Topics in quantum mechanics |
| title_full | Topics in quantum mechanics Floyd Williams |
| title_fullStr | Topics in quantum mechanics Floyd Williams |
| title_full_unstemmed | Topics in quantum mechanics Floyd Williams |
| title_short | Topics in quantum mechanics |
| title_sort | topics in quantum mechanics |
| topic | Mathematische Physik Quantentheorie Mathematical physics Quantum theory Quantenmechanik (DE-588)4047989-4 gnd |
| topic_facet | Mathematische Physik Quantentheorie Mathematical physics Quantum theory Quantenmechanik |
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