Generalized Sturmians and atomic spectra:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Hackensack, NJ [u.a.]
World Scientific
2006
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Klappentext |
| Beschreibung: | XVI, 240 S. graph. Darst. |
| ISBN: | 9812568069 9789812568069 |
Internformat
MARC
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| 020 | |a 9789812568069 |c pbk. |9 978-981-256806-9 | ||
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| 100 | 1 | |a Avery, James |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Generalized Sturmians and atomic spectra |c James Avery ; John Avery |
| 264 | 1 | |a Hackensack, NJ [u.a.] |b World Scientific |c 2006 | |
| 300 | |a XVI, 240 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 4 | |a Atomes - Spectre | |
| 650 | 4 | |a Schrödinger, Équation de | |
| 650 | 4 | |a Théorie quantique - Mathématiques | |
| 650 | 4 | |a Mathematik | |
| 650 | 4 | |a Quantentheorie | |
| 650 | 4 | |a Quantum theory |x Mathematics | |
| 650 | 4 | |a Schrödinger equation | |
| 650 | 4 | |a Atomic spectra | |
| 650 | 0 | 7 | |a Atomspektrum |0 (DE-588)4143334-8 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Sturm-Liouville-Problem |0 (DE-588)4489971-3 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Atomspektrum |0 (DE-588)4143334-8 |D s |
| 689 | 0 | 1 | |a Sturm-Liouville-Problem |0 (DE-588)4489971-3 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Avery, John |e Verfasser |4 aut | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-017378810 | ||
Datensatz im Suchindex
| _version_ | 1804138913144504320 |
|---|---|
| adam_text | Contents
Preface
xi
1.
HISTORICAL BACKGROUND
1
1.1
Sturm-Liouville theory
..................... 1
1.2
The introduction of Sturmians into quantum theory
.... 2
1.3
One-electron Coulomb Sturmians
............... 3
1.4
Generalized Sturmians and many-particle problems
..... 5
1.5
Use of generalized Sturmian basis sets to solve the many-
particle
Schrödinger
equation
................. 6
2.
MOMENTUM SPACE AND ITERATION
9
2.1
The d-dimensional
Schrödinger
equation in momentum space
9
2.2
Momentum-space orthonormality relations for Sturmian ba¬
sis sets
.............................. 11
2.3
Sturmian expansions of d-dimensional plane waves
..... 13
2.4
Iteration of the
Schrödinger
equation
............. 14
2.5
Generation of symmetry-adapted basis functions by iteration
16
2.6
Solutions to the Sturmian secular equations obtained entirely
by iteration
........................... 17
3.
GENERALIZED STURMIANS APPLIED TO ATOMIC
SPECTRA
19
3.1
Goscinskian configurations with weighted nuclear charges
. 19
3.2
Derivation of the secular equations
.............. 24
3.3
Symmetry-adapted basis sets for the 2-electron isoelectronic
series
............................... 26
viii
GENERALIZED
STURMIANS AND ATOMIC
SPECTRA
3.4
The large-Z approximation
................. 31
3.5
General symmetry-adapted basis sets derived from the
large-Z approximation
.................... 43
3.6
Symmetry-adapted basis functions from iteration
..... 44
4.
AUTOIONIZING STATES
47
4.1
Electron correlation and the molecule-like character of au-
toionizing states
........................ 47
4.2
Calculation of autoionizing states using generalized Stur-
mians
............................. 47
4.3
Higher series of 3S autoionizing states
........... 51
5.
CORE IONIZATION
57
5.1
Core ionization energies in the large-Z approximation
. . 57
5.2
Isonuclear series; piecewise-linear dependence of AE on
N 60
5.3
Core ionization energies for the 3-electron isoelectronic series
61
6.
STRONG EXTERNAL FIELDS
69
6.1
External electric fields
.................... 69
6.2
Anomalous states
....................... 70
6.3
Polarizabilities
........................ 75
6.4
Induced transition
dipole
moments
............. 75
6.5
External magnetic fields
................... 76
7.
RELATIVISTIC EFFECTS
79
7.1
Lorentz
invariance
and
4-
vectors
.............. 79
7.2
The Dirac equation for an electron in an external electro¬
magnetic potential
...................... 81
7.3
Time-independent problems
................. 82
7.4
The Dirac equation for an electron in the field of a nucleus
83
7.5
Relativistic formulation of the
Zeeman
and Paschen-Bach
effects
............................. 88
7.6
Relativistic many-electron Sturmians
............ 90
7.7
A simple example
....................... 95
7.
S Fine
structure of spectral lines
............... 101
8.
MOMENTUM SPACE; THE FOCK TRANSFORMATION
107
8.1
One-electron Coulomb Sturmians in direct space
..... 107
8.2
Fourier transforms of Coulomb Sturmians
......... 108
8.3
The Fock projection: Hyperspherical harmonics
...... 110
8.4
The momentum-space orthonormality relations revisited
.
Ill
CONTENTS ix
9.
HARMONIC POLYNOMIALS
117
9.1
Monomials, homogeneous polynomials, and harmonic poly¬
nomials
............................ 117
9.2
The canonical decomposition of a homogeneous polynomial
119
9.3
Generalized angular momentum
............... 122
9.4
Hyperangular integration
.................. 124
10.
HYPERSPHERICAL HARMONICS
129
10.1
The relationship between harmonic polynomials and hy-
perspherical harmonics
.................... 129
10.2
Construction of hyperspherical harmonics by means of har¬
monic projection
....................... 131
10.3
Hyperspherical harmonics in a 4-dimensional space
.... 132
10.4 Gegenbauer
polynomials
................... 134
10.5
Hyperspherical expansion of a d-dimensional plane wave
. 136
10.6
Alternative hyperspherical harmonics; The method of trees
139
11.
THE MANY-CENTER PROBLEM
153
11.1
The many-center one-electron problem
........... 153
11.2
Shibuya-Wulfman integrals
................. 154
11.3
Shibuya-Wulfman integrals and translations
........ 156
11.4
Matrix elements of the nuclear attraction potential
.... 157
11.5
The Sturmian secular equations for an electron moving in
a many-center potential
................... 158
11.6
Molecular spectra
....................... 161
Appendix A INTERELECTRON REPULSION INTEGRALS
167
A.I Procedure for evaluating the interelectron repulsion matrix
167
A.
2
Separation of the integrals into radial and angular parts
. 168
A.3 Evaluation of the radial integrals in terms of hypergeomet-
ric functions
.......................... 169
A.
4
Evaluation of the angular integrals by harmonic projection
170
A.
5
Relativistic interelectron repulsion integrals
........ 172
Appendix
В
GENERALIZED SLATER-CONDON RULES
175
B.I Introduction
.......................... 175
B.2 Slater determinants expressed in terms of the antisym-
metrizer
............................ 175
B.3 Scalar products between configurations
........... 176
B.4 One-electron operators
.................... 177
B.5 Two-electron operators
.................... 178
χ
GENERALIZED STURMIANS AND ATOMIC SPECTRA
Appendix
С
EXPANSION OF F(r) ABOUT ANOTHER CENTER
181
C.I Expansion of a displaced function of
r
in terms of
Gegen¬
bauer
polynomials
...................... 181
C.2 Expansion of plane waves using
Gegenbauer
polynomials
. 182
C.3 Explicit expressions for the displaced function in terms of
integrals over Bessel functions
................ 183
C.4 An alternative method, illustrated for the case where
d
= 3 184
С.
5
Closed-form differential expressions in terms of modified
spherical Bessel functions
.................. 186
Appendix
D
THE FOCK PROJECTION
187
D.I The one-electron
Schrödinger
equation in momentum space
187
D.2 The momentum-space wave equation for hydrogenlike
atoms
............................. 188
D.3 Projection of momentum-space onto a 4-dimensional
hypersphere
.......................... 188
D.4 Expansion of the kernel in terms of hyperspherical
harmonics
........................... 190
Appendix
E
THE GREEN S FUNCTION OF THE
SCHRÖDINGER
EQUATION
193
E.I The operator
—
Δ
+
p2K and its Green s function
...... 193
E.2 Conservation of symmetry under Fourier transformation
. 194
E.3 Conservation of symmetry under Green s function iteration
195
E.4 Alternative representations of the Green s function
.... 196
Appendix
F
CONFIGURATIONS BASED ON COULOMB
STURMIAN
ORBITALS 201
F.I Coulomb Sturmian spin-orbitals
............... 201
F.2 Generalized Shibuya-Wulfman integrals
.......... 203
F.3 An illustrative example
.................... 204
F.4 Ground states for the 2-electron isoelectronic series
.... 205
F.5 Generalization to molecular problems
............ 206
Appendix
G
NOTATION
209
Bibliography
213
Index
233
—
his book describes the generalized Sturmian method,
which offers a fresh approach to the calculation
of atomic spectra. Generalized Sturmians are
¡soenergetic solutions to an approximate many-electron
Schrodinger equation with a weighted potential. The
weighting factors are chosen in such a way as to make all of
the solutions correspond to a given energy. The advantage
of such an isoenergetic basis set is that every basis function
has the correct turning point behavior needed for efficient
synthesis of the wave function.
The book also discusses methods for automatic generation
of symmetry-adapted basis sets. Calculations using the
generalized Sturmian method are presented and compared
with experimental results from the NIST database. The
relationship of Sturmians to harmonic polynomials and
hyperspherical harmonics is also described. Methods for
treating angular functions and angular integrals by means
of harmonic projection are discussed, and these methods are
shown to be especially useful for relativistic calculations.
A final chapter discusses application of the generalized
Sturmian method to the calculation of molecular spectra.
|
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| classification_rvk | UK 1200 UK 4000 |
| ctrlnum | (OCoLC)70878007 (DE-599)BVBBV035458929 |
| dewey-full | 530.12 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530.12 |
| dewey-search | 530.12 |
| dewey-sort | 3530.12 |
| dewey-tens | 530 - Physics |
| discipline | Physik |
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| id | DE-604.BV035458929 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T21:35:44Z |
| institution | BVB |
| isbn | 9812568069 9789812568069 |
| language | English |
| lccn | 2006048636 |
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| physical | XVI, 240 S. graph. Darst. |
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| publisher | World Scientific |
| record_format | marc |
| spelling | Avery, James Verfasser aut Generalized Sturmians and atomic spectra James Avery ; John Avery Hackensack, NJ [u.a.] World Scientific 2006 XVI, 240 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Atomes - Spectre Schrödinger, Équation de Théorie quantique - Mathématiques Mathematik Quantentheorie Quantum theory Mathematics Schrödinger equation Atomic spectra Atomspektrum (DE-588)4143334-8 gnd rswk-swf Sturm-Liouville-Problem (DE-588)4489971-3 gnd rswk-swf Atomspektrum (DE-588)4143334-8 s Sturm-Liouville-Problem (DE-588)4489971-3 s DE-604 Avery, John Verfasser aut Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017378810&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017378810&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Avery, James Avery, John Generalized Sturmians and atomic spectra Atomes - Spectre Schrödinger, Équation de Théorie quantique - Mathématiques Mathematik Quantentheorie Quantum theory Mathematics Schrödinger equation Atomic spectra Atomspektrum (DE-588)4143334-8 gnd Sturm-Liouville-Problem (DE-588)4489971-3 gnd |
| subject_GND | (DE-588)4143334-8 (DE-588)4489971-3 |
| title | Generalized Sturmians and atomic spectra |
| title_auth | Generalized Sturmians and atomic spectra |
| title_exact_search | Generalized Sturmians and atomic spectra |
| title_full | Generalized Sturmians and atomic spectra James Avery ; John Avery |
| title_fullStr | Generalized Sturmians and atomic spectra James Avery ; John Avery |
| title_full_unstemmed | Generalized Sturmians and atomic spectra James Avery ; John Avery |
| title_short | Generalized Sturmians and atomic spectra |
| title_sort | generalized sturmians and atomic spectra |
| topic | Atomes - Spectre Schrödinger, Équation de Théorie quantique - Mathématiques Mathematik Quantentheorie Quantum theory Mathematics Schrödinger equation Atomic spectra Atomspektrum (DE-588)4143334-8 gnd Sturm-Liouville-Problem (DE-588)4489971-3 gnd |
| topic_facet | Atomes - Spectre Schrödinger, Équation de Théorie quantique - Mathématiques Mathematik Quantentheorie Quantum theory Mathematics Schrödinger equation Atomic spectra Atomspektrum Sturm-Liouville-Problem |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017378810&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017378810&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
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