Factorization Method in Quantum Mechanics
(Sprache: Englisch)
This book introduces the factorization method in quantum mechanics at an advanced level, with the aim of putting mathematical and physical concepts and techniques like the factorization method, Lie algebras, matrix elements and quantum control at the reader...
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This book introduces the factorization method in quantum mechanics at an advanced level, with the aim of putting mathematical and physical concepts and techniques like the factorization method, Lie algebras, matrix elements and quantum control at the reader s disposal. For this purpose, the text provides a comprehensive description of the factorization method and its wide applications in quantum mechanics which complements the traditional coverage found in quantum mechanics textbooks. This Work introduces the factorization method in quantum mechanics at an advanced level with an aim to put mathematical and physical concepts and techniques like the factorization method, Lie algebras, matrix elements and quantum control at the Reader s disposal. For this purpose a comprehensive description is provided of the factorization method and its wide applications in quantum mechanics which complements the traditional coverage found in the existing quantum mechanics textbooks. Related to this classic method are the supersymmetric quantum mechanics, shape invariant potentials and group theoretical approaches. It is no exaggeration to say that this method has become the milestone of these approaches. In fact the Author s driving force has been his desire to provide a comprehensive review volume that includes some new and significant results about the factorization method in quantum mechanics since the literature is inundated with scattered articles in this field, and to pave the Reader s way into this territory as rapidly as possible. The result: clear and understandable derivations with the necessary mathematical steps included so that the intelligent reader should be able to follow the text with relative ease, in particular when mathematically difficult material is presented.Audience:
Researchers and students of physics, mathematics, chemistry and electrical engineering.
Inhaltsverzeichnis zu „Factorization Method in Quantum Mechanics “
PART I - Introduction1. Introduction
PART II - Method
2. Theory
3. Lie Algebras SU(2) and SU(1,1)
PART III - Applications in Non-Relativistic Quantum mechanics
4. Harmonic Oscillator
5. Infinitely Deep Square-Well Potential
6. Morse Potential
7. Pschl-Teller Potential
8. Pseudoharmonic Oscillator
9. Algebraic Approach to an Electron in a Uniform Magnetic Field
10. Ring-Shaped Non-Spherical Oscillator
11. Generalized Laguerre Functions
12. New Non-Central Ring-Shaped Potential
13. Pschl-Teller Like Potential
14. Position-Dependent Mass Schrdinger Equation for a Singular Oscillator
PART IV - Applications in Relativistic Quantum Mechanics
15. SUSYQM and SKWB Approach to the Dirac Equation with a Coulomb Potential in 2+1 Dimensions
16. Realization of Dynamic Group for the Dirac Hydrogen-like Atom in 2+1 Dimensions
17. Algebraic Approach to Klein-Gordon Equation with the Hydrogen-like Atom in 1+2 Dimensions
18. SUSYQM and SKWB Approaches to Relativistic Dirac and Klein-Gordon Equations with Hyperbolic Potential
PART V - Quantum Control
19. Controllability of Quantum Systems for the Morse and PT Potentials with Dynamic Group SU(2)
20. Controllability of Quantum System for the PT-like Potential with Dynamic Group SU(1,1)
PART VI - Conclusions and Outlooks
21. Conclusions and outlooks
APPENDICES: A - Integral formulas of the confluent hypergeometric functions
B - Mean values rk for hydrogen-like atom
C - Commutator identities
D - Angular momentum operators in spherical coordinates
E - Confluent hypergeometric function
References
Index
Bibliographische Angaben
- Autor: Shi-Hai Dong
- 2007, 305 Seiten, Maße: 16 x 24,1 cm, Gebunden, Englisch
- Verlag: Springer Netherlands
- ISBN-10: 1402057954
- ISBN-13: 9781402057953
- Erscheinungsdatum: 12.04.2011
Sprache:
Englisch
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