Dynamical symmetry of the Kepler-Coulomb problem in classical and quantum mechanics: non-relativistic and relativistic
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York
Nova Science Publishers
2008
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIV, 150 S. |
| ISBN: | 9781604564990 |
Staff View
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| 245 | 1 | 0 | |a Dynamical symmetry of the Kepler-Coulomb problem in classical and quantum mechanics |b non-relativistic and relativistic |c Tamar T. Khachidze and Anzor A. Khelashvili |
| 264 | 1 | |a New York |b Nova Science Publishers |c 2008 | |
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Record in the Search Index
| _version_ | 1804138003368509440 |
|---|---|
| adam_text | Contents
Preface
Introduction
Chapter I
Chapter II
Chapter HI
Hidden (Dynamical) Symmetries in Classical Mechanics
1.1.
Constants of Motion as Generators of Infinitesimal
Transformations
1.2.
Derivation of Lrl Vector
1.
3.
Applications of LRL Vector in Classical Physics
(i) LRL Vector and the Orbit Equation
(ii). Algebraic Aspects of the Kepler Problem
1.
4.
Dynamical Symmetry for the
Isotropìe
Harmonic Oscillator
1.5.
Possible Generalizations of Dynamical Symmetries
1.
6.
Application of the Dynamical Evolution of
LRL Vector in General Central Case
[12]
Equations of Motion for General Central Forces
Equations of Motion for Arbitrary Forces
Summary Comments on Dynamical Symmetries in Classical
(Non-Relativistic) Mechanics
References
Hidden Symmetry in Classical Relativistic Mechanics
II.
1.
Auxiliary Problem: LRL Vector for a Modified Kepler Problem
II.
2.
The Laplace-Runge-Lenz Vector and the
Lorentz
Boost
II.
3.
Post-Newtonian Extensions of the LRL Vector
II.
4.
Relativistic Kepler Problem
References
Dynamical Symmetries in Non-Relativistic Quantum Mechanics
III.l. The Hydrogen Atom (General Consideration)
Algebraic Aspects of the Hydrogen Problem
[2]
ix
xi
1
1
9
11
11
12
14
18
22
23
25
27
28
29
29
35
40
43
45
47
47
48
vi
Contents
III.
2.
The Hydrogen Atom in the Momentum
54
Representation
52
Example of Application of the Momentum Representation:
54
Dynamical Symmetry of a Three Dimensional Wick-
Cutkosky Problem
54
HI.
3.
The Hydrogen Atom and the
Lorentz
Group
59
III.
4.
Three Dimensional
Isotropie
Harmonic Oscillator and Su(3)
61
References
65
Chapter IV A New Kind of Dynamical Symmetry
-
Supersymmetry
67
IV. I Supersymmetric Quantum Mechanics
67
IV.
2.
Supersymmetry and the Radial Problem
73
IV.
3.
Exact Supersymmetry in the Non-Relativistic Hydrogen Atom
75
References
79
Chapter V Relativistic Quantum Mechanics
81
V.l.
Supersymmetry in the Dirac Equation for the Coulomb
Potential
81
Appendix: Shape
Invariance (SI)
85
V.
2.
An Accidental Symmetry
Operator for the Dirac Equation
in the Coulomb Potential —from
Pauli
To Dirac
87
V.
3.
Physical Meaning and Some Applications of Johnson
—
Lippmann
Operator
92
Appendix: Calculation of Relevant Commutators
94
References
95
Chapter VI Generalizations to the Relativistic Dirac Hamiltonian
97
VI.
1.
Supersymmetry of the Dirac Hamiltonian for General Central
Potenetials
97
VI.2. Where Is the Harmonic Oscillator?
100
VI.
3.
Relativistic Quantum Mechanics of Dirac Oscillator
103
VI.
4.
The
Lorentz
-
Scalar Potential in the Dirac Equation
108
VI.
5.
Algebraic Derivation of the Spectrum of the Dirac
Hamiltonian for an Arbitrary Combination of the Lorentz-
Scalar and
Lorentz-
Vector Coulomb Potaential 111
Comments
115
References
115
Chapter
VII Some
Recent Developments
117
VII.
1
Hidden Supersymmetry of the Dirac-Coulomb Problem and
the Biedenharn Appoach
117
VII.
2
Some Practical Generalizations: The LRL Vector in the
Presence of an Electric Field
123
In the Form of Conclusions
124
References
127
Contents
vii
Bibliography
131
Parti
129
Part II Continuation
137
Index
145
|
| adam_txt |
Contents
Preface
Introduction
Chapter I
Chapter II
Chapter HI
Hidden (Dynamical) Symmetries in Classical Mechanics
1.1.
Constants of Motion as Generators of Infinitesimal
Transformations
1.2.
Derivation of Lrl Vector
1.
3.
Applications of LRL Vector in Classical Physics
(i) LRL Vector and the Orbit Equation
(ii). Algebraic Aspects of the Kepler Problem
1.
4.
Dynamical Symmetry for the
Isotropìe
Harmonic Oscillator
1.5.
Possible Generalizations of Dynamical Symmetries
1.
6.
Application of the Dynamical Evolution of
LRL Vector in General Central Case
[12]
Equations of Motion for General Central Forces
Equations of Motion for Arbitrary Forces
Summary Comments on Dynamical Symmetries in Classical
(Non-Relativistic) Mechanics
References
Hidden Symmetry in Classical Relativistic Mechanics
II.
1.
Auxiliary Problem: LRL Vector for a Modified Kepler Problem
II.
2.
The Laplace-Runge-Lenz Vector and the
Lorentz
Boost
II.
3.
Post-Newtonian Extensions of the LRL Vector
II.
4.
Relativistic Kepler Problem
References
Dynamical Symmetries in Non-Relativistic Quantum Mechanics
III.l. The Hydrogen Atom (General Consideration)
Algebraic Aspects of the Hydrogen Problem
[2]
ix
xi
1
1
9
11
11
12
14
18
22
23
25
27
28
29
29
35
40
43
45
47
47
48
vi
Contents
III.
2.
The Hydrogen Atom in the Momentum
54
Representation
52
Example of Application of the Momentum Representation:
54
Dynamical Symmetry of a Three Dimensional Wick-
Cutkosky Problem
54
HI.
3.
The Hydrogen Atom and the
Lorentz
Group
59
III.
4.
Three Dimensional
Isotropie
Harmonic Oscillator and Su(3)
61
References
65
Chapter IV A New Kind of Dynamical Symmetry
-
Supersymmetry
67
IV. I Supersymmetric Quantum Mechanics
67
IV.
2.
Supersymmetry and the Radial Problem
73
IV.
3.
Exact Supersymmetry in the Non-Relativistic Hydrogen Atom
75
References
79
Chapter V Relativistic Quantum Mechanics
81
V.l.
Supersymmetry in the Dirac Equation for the Coulomb
Potential
81
Appendix: Shape
Invariance (SI)
85
V.
2.
An "Accidental Symmetry
"
Operator for the Dirac Equation
in the Coulomb Potential —from
Pauli
To Dirac
87
V.
3.
Physical Meaning and Some Applications of Johnson
—
Lippmann
Operator
92
Appendix: Calculation of Relevant Commutators
94
References
95
Chapter VI Generalizations to the Relativistic Dirac Hamiltonian
97
VI.
1.
Supersymmetry of the Dirac Hamiltonian for General Central
Potenetials
97
VI.2. Where Is the Harmonic Oscillator?
100
VI.
3.
Relativistic Quantum Mechanics of Dirac Oscillator
103
VI.
4.
The
Lorentz
-
Scalar Potential in the Dirac Equation
108
VI.
5.
Algebraic Derivation of the Spectrum of the Dirac
Hamiltonian for an Arbitrary Combination of the Lorentz-
Scalar and
Lorentz-
Vector Coulomb Potaential 111
Comments
115
References
115
Chapter
VII Some
Recent Developments
117
VII.
1
Hidden Supersymmetry of the Dirac-Coulomb Problem and
the Biedenharn Appoach
117
VII.
2
Some Practical Generalizations: The LRL Vector in the
Presence of an Electric Field
123
In the Form of Conclusions
124
References
127
Contents
vii
Bibliography
131
Parti
129
Part II Continuation
137
Index
145 |
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| index_date | 2024-07-02T22:00:05Z |
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| spelling | Khachidze, Tamar T. Verfasser aut Dynamical symmetry of the Kepler-Coulomb problem in classical and quantum mechanics non-relativistic and relativistic Tamar T. Khachidze and Anzor A. Khelashvili New York Nova Science Publishers 2008 XIV, 150 S. txt rdacontent n rdamedia nc rdacarrier Quantentheorie Symmetry (Physics) Mechanics Quantum theory Quantentheorie (DE-588)4047992-4 gnd rswk-swf Mechanik (DE-588)4038168-7 gnd rswk-swf Symmetrie (DE-588)4058724-1 gnd rswk-swf Symmetrie (DE-588)4058724-1 s DE-604 Mechanik (DE-588)4038168-7 s Quantentheorie (DE-588)4047992-4 s Khelashvili, Anzor A. Verfasser aut Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016728128&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Khachidze, Tamar T. Khelashvili, Anzor A. Dynamical symmetry of the Kepler-Coulomb problem in classical and quantum mechanics non-relativistic and relativistic Quantentheorie Symmetry (Physics) Mechanics Quantum theory Quantentheorie (DE-588)4047992-4 gnd Mechanik (DE-588)4038168-7 gnd Symmetrie (DE-588)4058724-1 gnd |
| subject_GND | (DE-588)4047992-4 (DE-588)4038168-7 (DE-588)4058724-1 |
| title | Dynamical symmetry of the Kepler-Coulomb problem in classical and quantum mechanics non-relativistic and relativistic |
| title_auth | Dynamical symmetry of the Kepler-Coulomb problem in classical and quantum mechanics non-relativistic and relativistic |
| title_exact_search | Dynamical symmetry of the Kepler-Coulomb problem in classical and quantum mechanics non-relativistic and relativistic |
| title_exact_search_txtP | Dynamical symmetry of the Kepler-Coulomb problem in classical and quantum mechanics non-relativistic and relativistic |
| title_full | Dynamical symmetry of the Kepler-Coulomb problem in classical and quantum mechanics non-relativistic and relativistic Tamar T. Khachidze and Anzor A. Khelashvili |
| title_fullStr | Dynamical symmetry of the Kepler-Coulomb problem in classical and quantum mechanics non-relativistic and relativistic Tamar T. Khachidze and Anzor A. Khelashvili |
| title_full_unstemmed | Dynamical symmetry of the Kepler-Coulomb problem in classical and quantum mechanics non-relativistic and relativistic Tamar T. Khachidze and Anzor A. Khelashvili |
| title_short | Dynamical symmetry of the Kepler-Coulomb problem in classical and quantum mechanics |
| title_sort | dynamical symmetry of the kepler coulomb problem in classical and quantum mechanics non relativistic and relativistic |
| title_sub | non-relativistic and relativistic |
| topic | Quantentheorie Symmetry (Physics) Mechanics Quantum theory Quantentheorie (DE-588)4047992-4 gnd Mechanik (DE-588)4038168-7 gnd Symmetrie (DE-588)4058724-1 gnd |
| topic_facet | Quantentheorie Symmetry (Physics) Mechanics Quantum theory Mechanik Symmetrie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016728128&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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