Factorization method in quantum mechanics:
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| Main Author: | |
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| Format: | Book |
| Language: | English |
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Dordrecht
Springer
2007
|
| Series: | Fundamental theories of physics
150 |
| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Physical Description: | XIX, 297 S. graph. Darst. |
| ISBN: | 1402057954 9781402057953 |
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| 100 | 1 | |a Dong, Shi-Hai |d 1969- |e Verfasser |0 (DE-588)1018145125 |4 aut | |
| 245 | 1 | 0 | |a Factorization method in quantum mechanics |c by Shi-Hai Dong |
| 264 | 1 | |a Dordrecht |b Springer |c 2007 | |
| 300 | |a XIX, 297 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Fundamental theories of physics |v 150 | |
| 650 | 4 | |a Factorisation | |
| 650 | 4 | |a Théorie quantique | |
| 650 | 4 | |a Quantentheorie | |
| 650 | 4 | |a Factorization (Mathematics) | |
| 650 | 4 | |a Quantum theory | |
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Record in the Search Index
| _version_ | 1805091268005462016 |
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| adam_text |
Contents
Dedication
v
List of Figures
xiii
List of Tables
xv
Preface
xvii
Acknowledgments
xix
Part I Introduction
1.
INTRODUCTION
3
1
Basic review
3
2
Motivations and aims
11
Part II Method
2.
THEORY
15
1
Introduction
15
2
Formalism
15
3.
LIE ALGEBRAS SU(2) AND SU(
1,1) 17
1
Introduction
17
2
Abstract groups
19
3
Matrix representation
21
4
Properties of groups SU(2) and SO(3)
22
5
Properties of non-compact groups SO(2,
1)
and SU(1,
1) 23
6
Generators of Lie groups SU(2) and SU(
1, 1 ) 23
7
Irreducible representations
25
viii
FACTORIZATION METHOD IN QUANTUM MECHANICS
8
Irreducible unitary representations
28
9
Concluding remarks
30
Part III Applications in Non-relativistic Quantum Mechanics
4.
HARMONIC OSCILLATOR
35
1
Introduction
35
2
Exact solutions
36
3
Ladder operators
37
4
Bargmann-Segal transform
42
5
Single mode realization of dynamic group SU(1,
1) 42
6
Matrix elements
44
7
Coherent states
45
8
Franck-Condon factors
49
9
Concluding remarks
55
5.
INHNITELY DEEP SQUARE-WELL POTENTIAL
57
1
Introduction
57
2
Ladder operators for infinitely deep square-well potential
58
3
Realization of dynamic group SU(1,
1)
and matrix elements
60
4
Ladder operators for infinitely deep symmetric well potential
61
5
SUSYQM approach to infinitely deep square well potential
62
6
Perelomov coherent states
63
7
Barut-Girardello coherent states
67
8
Concluding remarks
70
6.
MORSE POTENTIAL
73
1
Introduction
73
2
Exact solutions
78
3
Ladder operators for the Morse potential
79
4
Realization of dynamic group SU(2)
82
5
Matrix elements
84
6
Harmonic limit
84
7
Franck-Condon factors
86
8
Transition probability
89
9
Realization of dynamic group SU(1,
1) 90
Contents ix
10
Concluding remarks
93
7. PÖSCHL-TELLER
POTENTIAL
95
1
Introduction
95
2
Exact solutions
97
3
Ladder operators
101
4
Realization of dynamic group SU(2)
103
5
Alternative approach to derive ladder operators
105
6
Harmonic limit
107
7
Expansions of the coordinate
χ
and momentum
ρ
from the
SU(2) generators
109
8
Concluding remarks
110
8.
PSEUDOHARMONIC OSCILLATOR 111
1
Introduction 111
2
Exact solutions in one dimension
112
3
Ladder operators
114
4
Barut-Girardello coherent states
117
5
Thermodynamic properties
118
6
Pseudoharmonic oscillator in arbitrary dimensions
122
7
Recurrence relations among matrix elements
129
8
Concluding remarks
135
9.
ALGEBRAIC APPROACH TO AN ELECTRON IN A UNIFORM
MAGNETIC FIELD
137
1
Introduction
137
2
Exact solutions
137
3
Ladder operators
139
4
Concluding remarks
142
10.
RING-SHAPED NON-SPHERICAL OSCILLATOR
143
1
Introduction
143
2
Exact solutions
143
3
Ladder operators
146
4
Realization of dynamic group
147
5
Concluding remarks
149
χ
FACTORIZATION METHOD IN QUANTUM MECHANICS
11.
GENERALIZED LAGUERRE FUNCTIONS
151
1
Introduction
151
2
Generalized Laguerre functions
151
3
Ladder operators and realization of dynamic group SU(
1,1) 153
4
Concluding remarks
155
12.
NEW
NONCENTRAL
RING-SHAPED POTENTIAL
157
1
Introduction
157
2
Bound states
158
3
Ladder operators
161
4
Mean values
162
5
Continuum states
165
6
Concluding remarks
168
13.
PÖSCHL-TELLER
LIKE POTENTIAL
169
1
Introduction
169
2
Exact solutions
169
3
Ladder operators
171
4
Realization of dynamic group and matrix elements
173
5
Infinitely square well and harmonic limits
174
6
Concluding remarks
176
14.
POSITION-DEPENDENT MASS
SCHRÖDINGER
EQUATION
FOR A SINGULAR OSCILLATOR
177
1
Introduction
177
2
Position-dependent effective mass
Schrödinger
equation for
harmonic oscillator
178
3
Singular oscillator with a position-dependent effective mass
179
4
Complete solutions
181
5
Another position-dependent effective mass
183
6
Concluding remarks
184
Contents xi
Part IV
Applications in Relativistic Quantum
Mechanics
15.
SUS YQM AND S WKB
APPROACH TO THE DIRAC EQUATION
WITH A COULOMB POTENTIAL IN
2+1
DIMENSIONS
187
1
Introduction
187
2
Dirac equation in
2 +1
dimensions
188
3
Exact solutions
189
4
SUSYQM and SWKB approaches to Coulomb problem
193
5
Alternative method to derive exact eigenfunctions
195
6
Concluding remarks
198
16.
REALIZATION OF DYNAMIC GROUP FOR
THE DIRAC HYDROGEN-LIKE ATOM IN
2+1
DIMENSIONS
201
1
Introduction
201
2
Realization of dynamic group SU(1,
1) 201
3
Concluding remarks
206
17.
ALGEBRAIC APPROACH TO KLEIN-GORDON
EQUATION WITH THE HYDROGEN-LIKE
ATOM IN
2+1
DIMENSIONS
207
1
Introduction
207
2
Exact solutions
207
3
Realization of dynamic group SU(1,
1) 209
4
Concluding remarks
211
18.
SUSYQM AND SWKB APPROACHES TO RELATIVISTIC
DIRAC AND KLEIN-GORDON EQUATIONS WITH HYPERBOLIC
POTENTIAL
213
1
Introduction
213
2
Relativistic Klein-Gordon and Dirac equations with hyperbolic
potential Vo tanh2
{r/ď)
214
3
SUSYQM and SWKB approaches to obtain eigenvalues
216
4
Complete solutions by traditional method
217
5
Harmonic limit
221
6
Concluding remarks
222
xii
FACTORIZATION METHOD IN QUANTUM MECHANICS
Part V Quantum Control
19.
CONTROLLABILITY OF QUANTUM SYSTEMS FOR THE
MORSE AND PT POTENTIALS WITH DYNAMIC GROUP SU(2)
225
1
Introduction
225
2
Preliminaries on control theory
226
3
Analysis of the controllability
227
4
Concluding remarks
228
20.
CONTROLLABILITY OF QUANTUM SYSTEM FOR THE
PT-LIKE POTENTIAL WITH DYNAMIC GROUP SU(
1, 1 ) 229
1
Introduction
229
2
Preliminaries on the control theory
230
3
Analysis of controllability
233
4
Concluding remarks
234
Part VI Conclusions and Outlooks
21.
CONCLUSIONS AND OUTLOOKS
237
1
Conclusions
237
2
Outlooks
238
Appendices
239
A Integral formulas of the confluent hypergeometric functions
239
В
Mean values rk for hydrogen-like atom
243
С
Commutator identities
247
D
Angular momentum operators in spherical coordinates
249
E
Confluent hypergeometric function
251
References
255
Index
295 |
| adam_txt |
Contents
Dedication
v
List of Figures
xiii
List of Tables
xv
Preface
xvii
Acknowledgments
xix
Part I Introduction
1.
INTRODUCTION
3
1
Basic review
3
2
Motivations and aims
11
Part II Method
2.
THEORY
15
1
Introduction
15
2
Formalism
15
3.
LIE ALGEBRAS SU(2) AND SU(
1,1) 17
1
Introduction
17
2
Abstract groups
19
3
Matrix representation
21
4
Properties of groups SU(2) and SO(3)
22
5
Properties of non-compact groups SO(2,
1)
and SU(1,
1) 23
6
Generators of Lie groups SU(2) and SU(
1, 1 ) 23
7
Irreducible representations
25
viii
FACTORIZATION METHOD IN QUANTUM MECHANICS
8
Irreducible unitary representations
28
9
Concluding remarks
30
Part III Applications in Non-relativistic Quantum Mechanics
4.
HARMONIC OSCILLATOR
35
1
Introduction
35
2
Exact solutions
36
3
Ladder operators
37
4
Bargmann-Segal transform
42
5
Single mode realization of dynamic group SU(1,
1) 42
6
Matrix elements
44
7
Coherent states
45
8
Franck-Condon factors
49
9
Concluding remarks
55
5.
INHNITELY DEEP SQUARE-WELL POTENTIAL
57
1
Introduction
57
2
Ladder operators for infinitely deep square-well potential
58
3
Realization of dynamic group SU(1,
1)
and matrix elements
60
4
Ladder operators for infinitely deep symmetric well potential
61
5
SUSYQM approach to infinitely deep square well potential
62
6
Perelomov coherent states
63
7
Barut-Girardello coherent states
67
8
Concluding remarks
70
6.
MORSE POTENTIAL
73
1
Introduction
73
2
Exact solutions
78
3
Ladder operators for the Morse potential
79
4
Realization of dynamic group SU(2)
82
5
Matrix elements
84
6
Harmonic limit
84
7
Franck-Condon factors
86
8
Transition probability
89
9
Realization of dynamic group SU(1,
1) 90
Contents ix
10
Concluding remarks
93
7. PÖSCHL-TELLER
POTENTIAL
95
1
Introduction
95
2
Exact solutions
97
3
Ladder operators
101
4
Realization of dynamic group SU(2)
103
5
Alternative approach to derive ladder operators
105
6
Harmonic limit
107
7
Expansions of the coordinate
χ
and momentum
ρ
from the
SU(2) generators
109
8
Concluding remarks
110
8.
PSEUDOHARMONIC OSCILLATOR 111
1
Introduction 111
2
Exact solutions in one dimension
112
3
Ladder operators
114
4
Barut-Girardello coherent states
117
5
Thermodynamic properties
118
6
Pseudoharmonic oscillator in arbitrary dimensions
122
7
Recurrence relations among matrix elements
129
8
Concluding remarks
135
9.
ALGEBRAIC APPROACH TO AN ELECTRON IN A UNIFORM
MAGNETIC FIELD
137
1
Introduction
137
2
Exact solutions
137
3
Ladder operators
139
4
Concluding remarks
142
10.
RING-SHAPED NON-SPHERICAL OSCILLATOR
143
1
Introduction
143
2
Exact solutions
143
3
Ladder operators
146
4
Realization of dynamic group
147
5
Concluding remarks
149
χ
FACTORIZATION METHOD IN QUANTUM MECHANICS
11.
GENERALIZED LAGUERRE FUNCTIONS
151
1
Introduction
151
2
Generalized Laguerre functions
151
3
Ladder operators and realization of dynamic group SU(
1,1) 153
4
Concluding remarks
155
12.
NEW
NONCENTRAL
RING-SHAPED POTENTIAL
157
1
Introduction
157
2
Bound states
158
3
Ladder operators
161
4
Mean values
162
5
Continuum states
165
6
Concluding remarks
168
13.
PÖSCHL-TELLER
LIKE POTENTIAL
169
1
Introduction
169
2
Exact solutions
169
3
Ladder operators
171
4
Realization of dynamic group and matrix elements
173
5
Infinitely square well and harmonic limits
174
6
Concluding remarks
176
14.
POSITION-DEPENDENT MASS
SCHRÖDINGER
EQUATION
FOR A SINGULAR OSCILLATOR
177
1
Introduction
177
2
Position-dependent effective mass
Schrödinger
equation for
harmonic oscillator
178
3
Singular oscillator with a position-dependent effective mass
179
4
Complete solutions
181
5
Another position-dependent effective mass
183
6
Concluding remarks
184
Contents xi
Part IV
Applications in Relativistic Quantum
Mechanics
15.
SUS YQM AND S WKB
APPROACH TO THE DIRAC EQUATION
WITH A COULOMB POTENTIAL IN
2+1
DIMENSIONS
187
1
Introduction
187
2
Dirac equation in
2 +1
dimensions
188
3
Exact solutions
189
4
SUSYQM and SWKB approaches to Coulomb problem
193
5
Alternative method to derive exact eigenfunctions
195
6
Concluding remarks
198
16.
REALIZATION OF DYNAMIC GROUP FOR
THE DIRAC HYDROGEN-LIKE ATOM IN
2+1
DIMENSIONS
201
1
Introduction
201
2
Realization of dynamic group SU(1,
1) 201
3
Concluding remarks
206
17.
ALGEBRAIC APPROACH TO KLEIN-GORDON
EQUATION WITH THE HYDROGEN-LIKE
ATOM IN
2+1
DIMENSIONS
207
1
Introduction
207
2
Exact solutions
207
3
Realization of dynamic group SU(1,
1) 209
4
Concluding remarks
211
18.
SUSYQM AND SWKB APPROACHES TO RELATIVISTIC
DIRAC AND KLEIN-GORDON EQUATIONS WITH HYPERBOLIC
POTENTIAL
213
1
Introduction
213
2
Relativistic Klein-Gordon and Dirac equations with hyperbolic
potential Vo tanh2
{r/ď)
214
3
SUSYQM and SWKB approaches to obtain eigenvalues
216
4
Complete solutions by traditional method
217
5
Harmonic limit
221
6
Concluding remarks
222
xii
FACTORIZATION METHOD IN QUANTUM MECHANICS
Part V Quantum Control
19.
CONTROLLABILITY OF QUANTUM SYSTEMS FOR THE
MORSE AND PT POTENTIALS WITH DYNAMIC GROUP SU(2)
225
1
Introduction
225
2
Preliminaries on control theory
226
3
Analysis of the controllability
227
4
Concluding remarks
228
20.
CONTROLLABILITY OF QUANTUM SYSTEM FOR THE
PT-LIKE POTENTIAL WITH DYNAMIC GROUP SU(
1, 1 ) 229
1
Introduction
229
2
Preliminaries on the control theory
230
3
Analysis of controllability
233
4
Concluding remarks
234
Part VI Conclusions and Outlooks
21.
CONCLUSIONS AND OUTLOOKS
237
1
Conclusions
237
2
Outlooks
238
Appendices
239
A Integral formulas of the confluent hypergeometric functions
239
В
Mean values rk for hydrogen-like atom
243
С
Commutator identities
247
D
Angular momentum operators in spherical coordinates
249
E
Confluent hypergeometric function
251
References
255
Index
295 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Dong, Shi-Hai 1969- |
| author_GND | (DE-588)1018145125 |
| author_facet | Dong, Shi-Hai 1969- |
| author_role | aut |
| author_sort | Dong, Shi-Hai 1969- |
| author_variant | s h d shd |
| building | Verbundindex |
| bvnumber | BV035110483 |
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| callnumber-sort | QC 3174.17 F3 |
| callnumber-subject | QC - Physics |
| classification_rvk | UK 3000 UK 4000 |
| ctrlnum | (OCoLC)124038194 (DE-599)BSZ277321824 |
| dewey-full | 530.12 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530.12 |
| dewey-search | 530.12 |
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| dewey-tens | 530 - Physics |
| discipline | Physik |
| discipline_str_mv | Physik |
| format | Book |
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| id | DE-604.BV035110483 |
| illustrated | Illustrated |
| index_date | 2024-07-02T22:17:16Z |
| indexdate | 2024-07-20T09:53:00Z |
| institution | BVB |
| isbn | 1402057954 9781402057953 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016778314 |
| oclc_num | 124038194 |
| open_access_boolean | |
| owner | DE-703 DE-11 |
| owner_facet | DE-703 DE-11 |
| physical | XIX, 297 S. graph. Darst. |
| publishDate | 2007 |
| publishDateSearch | 2007 |
| publishDateSort | 2007 |
| publisher | Springer |
| record_format | marc |
| series | Fundamental theories of physics |
| series2 | Fundamental theories of physics |
| spelling | Dong, Shi-Hai 1969- Verfasser (DE-588)1018145125 aut Factorization method in quantum mechanics by Shi-Hai Dong Dordrecht Springer 2007 XIX, 297 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Fundamental theories of physics 150 Factorisation Théorie quantique Quantentheorie Factorization (Mathematics) Quantum theory Faktorisierung (DE-588)4128927-4 gnd rswk-swf Quantenmechanik (DE-588)4047989-4 gnd rswk-swf Quantenmechanik (DE-588)4047989-4 s Faktorisierung (DE-588)4128927-4 s DE-604 Erscheint auch als Online-Ausgabe 978-1-402-05796-0 Fundamental theories of physics 150 (DE-604)BV000012461 150 text/html http://deposit.dnb.de/cgi-bin/dokserv?id=2887497&prov=M&dok_var=1&dok_ext=htm Inhaltstext Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016778314&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Dong, Shi-Hai 1969- Factorization method in quantum mechanics Fundamental theories of physics Factorisation Théorie quantique Quantentheorie Factorization (Mathematics) Quantum theory Faktorisierung (DE-588)4128927-4 gnd Quantenmechanik (DE-588)4047989-4 gnd |
| subject_GND | (DE-588)4128927-4 (DE-588)4047989-4 |
| title | Factorization method in quantum mechanics |
| title_auth | Factorization method in quantum mechanics |
| title_exact_search | Factorization method in quantum mechanics |
| title_exact_search_txtP | Factorization method in quantum mechanics |
| title_full | Factorization method in quantum mechanics by Shi-Hai Dong |
| title_fullStr | Factorization method in quantum mechanics by Shi-Hai Dong |
| title_full_unstemmed | Factorization method in quantum mechanics by Shi-Hai Dong |
| title_short | Factorization method in quantum mechanics |
| title_sort | factorization method in quantum mechanics |
| topic | Factorisation Théorie quantique Quantentheorie Factorization (Mathematics) Quantum theory Faktorisierung (DE-588)4128927-4 gnd Quantenmechanik (DE-588)4047989-4 gnd |
| topic_facet | Factorisation Théorie quantique Quantentheorie Factorization (Mathematics) Quantum theory Faktorisierung Quantenmechanik |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=2887497&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016778314&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000012461 |
| work_keys_str_mv | AT dongshihai factorizationmethodinquantummechanics |