Semiclassical theory of atoms:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin u.a.
Springer
1988
|
| Series: | Lecture notes in physics
300 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VII, 401 S. |
| ISBN: | 3540192042 0387192042 |
Staff View
MARC
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| 100 | 1 | |a Englert, Berthold-Georg |d 1953- |e Verfasser |0 (DE-588)13834504X |4 aut | |
| 245 | 1 | 0 | |a Semiclassical theory of atoms |c Berthold-Georg Englert |
| 264 | 1 | |a Berlin u.a. |b Springer |c 1988 | |
| 300 | |a VII, 401 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Lecture notes in physics |v 300 | |
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Record in the Search Index
| _version_ | 1804115318120906752 |
|---|---|
| adam_text | Table
of Contents
Chapter One. Introduction
........................................ 1
Atomic units
.................................................. 2
Bohr atoms
.................................................... 4
Traces and phase-space integrals
.............................. 10
Bohr atoms with shielding
..................................... 11
The effective potential
....................................... 13
Size of atoms
................................................. 21
Problems
...................................................... 24
Chapter Two. Thomas-Fermi Model
.................................. 27
General formalism
............................................. 27
The TF model
.................................................. 33
Neutral TF atoms
.............................................. 37
Maximum property of the TF potential functional
............... 39
An electrostatic analogy
...................................... 41
TP
density functional
......................................... 43
Minimum property of the TF density functional
................. 45
Upper bounds on
В
............................................. 46
Lower bounds on
В
............................................. 50
Binding energy of neutral TF atoms
............................ 54
TF function
F (x)
.............................................. 56
Scaling properties of the TF model
............................ 66
Highly ionized TF atoms
....................................... 73
Weakly ionized TF atoms
....................................... 80
Arbitrarily ionized TF atoms
.................................. 96
Validity of the TF model
...................................... 99
Density and potential functionals
............................. 104
Relation between the TF approximation and
Hartree
s
method
—. 119
Problems
...................................................... 124
Chapter Three. Strongly Bound Electrons
.......................... 130
Qualitative argument
.......................................... 130
First quantitative derivation of Scott
s
correction
........... 131
Scott
s
original argument
..................................... 138
TFS energy functional
......................................... 139
TFS density
................................................... 146
VI
Consistency
.....................·............................. 148
Scaling properties of the TFS model
........................... 155
Second quantitative derivation of Scott s correction
.......... 158
Some implications concerning energy
........................... 162
Electron density at the site of the nucleus
................... 164
Numerical procedure
........................................... 168
Numerical results for neutral mercury
......................... 170
Problems
...................................................... 173
Chapter Four. Quantum Corrections and Exchange
................... 175
Qualitative arguments
......................................... 176
Quantum corrections I (time transformation function)
.......... 177
Quantum corrections II (leading energy correction)
............ 190
The
von Weizsäcker
term
....................................... 194
Quantum corrections III (energy)
.............................. 196
Airy averages
................................................. 199
Validity of the TF approximation
.............................. 207
Quantum corrected E1
(V+ç
)..................................... 210
Quantum corrected density
..................................... 213
Exchange I (general)
.......................................... 221
Self energy
................................................... 225
Exchange II (leading correction)
.............................. 225
History
....................................................... 230
Energy corrections for ions
................................... 232
Ionization energies
........................................... 236
Minimal binding energies (chemical potentials)
................ 239
Shielding of the nuclear magnetic moment
...................... 241
Simplified new differential equation
(ES
model)
............... 244
An application of the
ES
model. Diamagnetic susceptibilities..
255
Improved
(?) ES
model. Electric polarizabilities
.............. 260
Exchange III
.
(Exchange potential)
............................ 275
New differential equation
..................................... 278
Small distances
............................................... 282
Large distances
............................................... 283
Numerical results
............................................. 286
Problems
...................................................... 293
Chapter Five. Shell Structure
.................................... 295
Experimental evidence
......................................... 297
Qualitative arguments
......................................... 299
Bohr atoms
.................................................... 300
VII
TF
quantization
............................................... 305
Fourier formulation
........................................... 312
Isolating the TF contribution
................................. 314
Lines of degeneracy
........................................... 315
Classical orbits
.............................................. 320
Degeneracy in the TF potential
.................................323
TF degeneracy and the systematics of the Periodic Table
....... 327
General features of
N ....................................... 329
General features of
E
....................................... 333
qu
Linear degeneracy. Scott correction
........................... 335
Perturbative approach to
E
.·............................... 336
rr
osc
А
-quantized TF model
.......................................... 338
j
5^0
terms. Leading energy oscillation
......................... 342
Fresnel integrals
............................................. 347
λ
oscillations
................................................ 351
ν
oscillations
................................................ 358
Semiclassical prediction for
E
............................. 360
ť
osc
Other manifestations of shell structure
....................... 363
Problems
...................................................... 367
Chapter Six. Miscellanea
......................................... 370
Relativistic corrections
...................................... 370
Kohn-Sham equation
............................................ 377
Wigner
s
phase-space functions
................................ 379
Problems
...................................................... 381
Footnotes
........................................................ 383
Chapter One
................................................... 383
Chapter Two
................................................... 384
Chapter Three
................................................. 387
Chapter Four
.................................................. 389
Chapter Five
.................................................. 394
Chapter Six
................................................... 395
Index
............................................................ 397
Names
......................................................... 397
Subjects
...................................................... 398
|
| any_adam_object | 1 |
| author | Englert, Berthold-Georg 1953- |
| author_GND | (DE-588)13834504X |
| author_facet | Englert, Berthold-Georg 1953- |
| author_role | aut |
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| classification_rvk | UD 8220 UM 2000 |
| classification_tum | PHY 501f |
| ctrlnum | (OCoLC)443390253 (DE-599)BVBBV000864090 |
| discipline | Physik |
| format | Book |
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| id | DE-604.BV000864090 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:20:42Z |
| institution | BVB |
| isbn | 3540192042 0387192042 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-000542670 |
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| owner_facet | DE-12 DE-91G DE-BY-TUM DE-19 DE-BY-UBM DE-355 DE-BY-UBR DE-20 DE-29T DE-706 DE-83 DE-188 DE-11 |
| physical | VII, 401 S. |
| publishDate | 1988 |
| publishDateSearch | 1988 |
| publishDateSort | 1988 |
| publisher | Springer |
| record_format | marc |
| series | Lecture notes in physics |
| series2 | Lecture notes in physics |
| spelling | Englert, Berthold-Georg 1953- Verfasser (DE-588)13834504X aut Semiclassical theory of atoms Berthold-Georg Englert Berlin u.a. Springer 1988 VII, 401 S. txt rdacontent n rdamedia nc rdacarrier Lecture notes in physics 300 Quasiklassisches Modell (DE-588)4318601-4 gnd rswk-swf Thomas-Fermi-Modell (DE-588)4185321-0 gnd rswk-swf Atom (DE-588)4003412-4 gnd rswk-swf Thomas-Fermi-Modell (DE-588)4185321-0 s DE-604 Atom (DE-588)4003412-4 s Quasiklassisches Modell (DE-588)4318601-4 s Lecture notes in physics 300 (DE-604)BV000003166 300 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000542670&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Englert, Berthold-Georg 1953- Semiclassical theory of atoms Lecture notes in physics Quasiklassisches Modell (DE-588)4318601-4 gnd Thomas-Fermi-Modell (DE-588)4185321-0 gnd Atom (DE-588)4003412-4 gnd |
| subject_GND | (DE-588)4318601-4 (DE-588)4185321-0 (DE-588)4003412-4 |
| title | Semiclassical theory of atoms |
| title_auth | Semiclassical theory of atoms |
| title_exact_search | Semiclassical theory of atoms |
| title_full | Semiclassical theory of atoms Berthold-Georg Englert |
| title_fullStr | Semiclassical theory of atoms Berthold-Georg Englert |
| title_full_unstemmed | Semiclassical theory of atoms Berthold-Georg Englert |
| title_short | Semiclassical theory of atoms |
| title_sort | semiclassical theory of atoms |
| topic | Quasiklassisches Modell (DE-588)4318601-4 gnd Thomas-Fermi-Modell (DE-588)4185321-0 gnd Atom (DE-588)4003412-4 gnd |
| topic_facet | Quasiklassisches Modell Thomas-Fermi-Modell Atom |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000542670&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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