Regularity and approximability of electronic wave functions:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2010
|
| Schriftenreihe: | Lecture notes in mathematics
2000 |
| Schlagworte: | |
| Online-Zugang: | Inhaltstext Inhaltsverzeichnis |
| Beschreibung: | VIII, 182 S. |
| ISBN: | 9783642122477 |
Internformat
MARC
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Datensatz im Suchindex
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CONTENTS 1 INTRODUCTION AND OUTLINE 1 2 FOURIER ANALYSIS 13 2.1 RAPIDLY
DECREASING FUNCTIONS 13 2.2 INTEGRABLE AND SQUARE INTEGRABLE FUNCTIONS
17 2.3 SPACES OF WEAKLY DIFFERENTIABLE FUNCTIONS 20 2.4 FOURIER AND
LAPLACE TRANSFORMATION 25 3 THE BASICS OF QUANTUM MECHANICS 27 3. 1
WAVES, WAVE PACKETS, AND WAVE EQUATIONS 28 3.2 THE SCHROEDINGER EQUATION
FOR A FREE PARTICLE 29 3.3 THE MATHEMATICAL FRAMEWORK OF QUANTUM
MECHANICS 32 3.4 THE HARMONIC OSCILLATOR AND ITS EIGENFUNCTIONS 37 3.5
THE WEAK FORM OF THE SCHROEDINGER EQUATION 44 3.6 THE QUANTUM MECHANICS
OF MULTI-PARTICLE SYSTEMS 46 4 THE ELECTRONIC SCHROEDINGER EQUATION 51 4.
1 THE HARDY INEQUALITY AND THE INTERACTION ENERGY 52 4.2 SPIN AND THE
PAULI PRINCIPLE 55 5 SPECTRUM AND EXPONENTIAL DECAY 59 5. 1 THE MINIMUM
ENERGY AND THE IONIZATION THRESHOLD 60 5.2 DISCRETE AND ESSENTIAL
SPECTRUM 61 5.3 THE RAYLEIGH-RITZ METHOD 71 5.4 THE LOWER BOUND OF THE
ESSENTIAL SPECTRUM 78 5.5 THE EXPONENTIAL DECAY OF THE EIGENFUNCTIONS 82
6 EXISTENCE AND DECAY OF MIXED DERIVATIVES 87 6. 1 A MODIFIED EIGENVALUE
PROBLEM 88 6.2 SPACES OF FUNCTIONS WITH HIGH-ORDER MIXED DERIVATIVES 91
6. BIBLIOGRAFISCHE INFORMATIONEN HTTP://D-NB.INFO/1000569209
DIGITALISIERT DURCH 181 VIN CONTENTS 6.5 THE REGULARITY OF THE WEIGHTED
EIGENFUNCTIONS 103 6.6 ATOMS AS MODEL SYSTEMS ILL 6.7 THE EXPONENTIAL
DECAY OF THE MIXED DERIVATIVES 115 7 EIGENFUNCTION EXPANSIONS 117 7.1
DISCRETE REGULARITY 118 7.2 ANTISYMMETRY 123 7.3 HYPERBOLIC CROSS SPACES
1 24 8 CONVERGENCE RATES AND COMPLEXITY BOUNDS 127 8. 1 THE GROWTH OF
THE EIGENVALUES IN THE 3D-CASE 128 8.2 A DIMENSION ESTIMATE FOR
HYPERBOLIC CROSS SPACES 131 8.3 AN ASYMPTOTIC BOUND 134 8.4 A PROOF OF
THE ESTIMATE FOR THE PARTITION NUMBERS 135 8.5 THE COMPLEXITY OF THE
QUANTUM N-BODY PROBLEM 1 39 9 THE RADIAL-ANGULAR DECOMPOSITION 141 9. 1
THREE-DIMENSIONAL SPHERICAL HARMONICS 142 9.2 THE DECOMPOSITION OF
N-PARTICLE WAVE FUNCTIONS 151 9.3 THE RADIAL SCHROEDINGER EQUATION 154
9.4 AN EXCURSUS TO THE COULOMB PROBLEM 159 9.5 THE HARMONIC OSCILLATOR
162 9.6 EIGENFUNCTION EXPANSIONS REVISITED 164 9.7 APPROXIMATION BY
GAUSS FUNCTIONS 165 9.8 THE EFFECT OF SCALING 167 APPENDIX: THE STANDARD
BASIS OF THE SPHERICAL HARMONICS 1 70 REFERENCES 177 INDEX |
| any_adam_object | 1 |
| author | Yserentant, Harry 1952- |
| author_GND | (DE-588)141509813 |
| author_facet | Yserentant, Harry 1952- |
| author_role | aut |
| author_sort | Yserentant, Harry 1952- |
| author_variant | h y hy |
| building | Verbundindex |
| bvnumber | BV036515896 |
| classification_rvk | SI 850 |
| classification_tum | MAT 356f MAT 410f |
| ctrlnum | (OCoLC)699727133 (DE-599)DNB1000569209 |
| dewey-full | 515.353 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.353 |
| dewey-search | 515.353 |
| dewey-sort | 3515.353 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| isbn | 9783642122477 |
| language | English |
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| physical | VIII, 182 S. |
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| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spelling | Yserentant, Harry 1952- Verfasser (DE-588)141509813 aut Regularity and approximability of electronic wave functions Harry Yserentant Berlin [u.a.] Springer 2010 VIII, 182 S. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 2000 Approximation (DE-588)4002498-2 gnd rswk-swf Schrödinger-Gleichung (DE-588)4053332-3 gnd rswk-swf Wellenfunktion (DE-588)4189547-2 gnd rswk-swf Regularität (DE-588)4049074-9 gnd rswk-swf Schrödinger-Gleichung (DE-588)4053332-3 s Wellenfunktion (DE-588)4189547-2 s Approximation (DE-588)4002498-2 s Regularität (DE-588)4049074-9 s DE-604 Erscheint auch als Online-Ausgabe 978-3-642-12248-4 Lecture notes in mathematics 2000 (DE-604)BV000676446 2000 text/html http://deposit.dnb.de/cgi-bin/dokserv?id=3435227&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=020438013&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Yserentant, Harry 1952- Regularity and approximability of electronic wave functions Lecture notes in mathematics Approximation (DE-588)4002498-2 gnd Schrödinger-Gleichung (DE-588)4053332-3 gnd Wellenfunktion (DE-588)4189547-2 gnd Regularität (DE-588)4049074-9 gnd |
| subject_GND | (DE-588)4002498-2 (DE-588)4053332-3 (DE-588)4189547-2 (DE-588)4049074-9 |
| title | Regularity and approximability of electronic wave functions |
| title_auth | Regularity and approximability of electronic wave functions |
| title_exact_search | Regularity and approximability of electronic wave functions |
| title_full | Regularity and approximability of electronic wave functions Harry Yserentant |
| title_fullStr | Regularity and approximability of electronic wave functions Harry Yserentant |
| title_full_unstemmed | Regularity and approximability of electronic wave functions Harry Yserentant |
| title_short | Regularity and approximability of electronic wave functions |
| title_sort | regularity and approximability of electronic wave functions |
| topic | Approximation (DE-588)4002498-2 gnd Schrödinger-Gleichung (DE-588)4053332-3 gnd Wellenfunktion (DE-588)4189547-2 gnd Regularität (DE-588)4049074-9 gnd |
| topic_facet | Approximation Schrödinger-Gleichung Wellenfunktion Regularität |
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