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110707s2011 ne | s |||| 0|eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| International Standard Book Number |
9789400719170 |
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978-94-007-1917-0 |
| 050 #4 - LIBRARY OF CONGRESS CALL NUMBER |
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| Classification number |
QC173.96-174.52 |
| 082 04 - DEWEY DECIMAL CLASSIFICATION NUMBER |
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| Classification number |
530.12 |
| Edition number |
23 |
| 264 #1 - |
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| -- |
Dordrecht : |
| -- |
Springer Netherlands, |
| -- |
2011. |
| 912 ## - |
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| -- |
ZDB-2-PHA |
| 100 1# - MAIN ENTRY--PERSONAL NAME |
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| Personal name |
Dong, Shi-Hai. |
| Relator term |
author. |
| 245 10 - IMMEDIATE SOURCE OF ACQUISITION NOTE |
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| Title |
Wave Equations in Higher Dimensions |
| Medium |
[electronic resource] / |
| Statement of responsibility, etc |
by Shi-Hai Dong. |
| 300 ## - PHYSICAL DESCRIPTION |
|---|
| Extent |
XXV, 295p. 49 illus. |
| Other physical details |
online resource. |
| 505 0# - FORMATTED CONTENTS NOTE |
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| Formatted contents note |
Part I (Introduction) -- Part II (Theory). - 2. Special orthogonal groups (Introduction; Abstract groups;Orthogonal group SO(n); Tensor representations of the SO(n); \Gamma matrix groups; Spinor representations of the SO(n); Concluding remarks) -- 3. Rotational symmetry and Schrödinger equation in N-dimensional space (Introduction; Rotation operator; Orbital angular momentum operators; The linear momentum operators;Radial momentum operator; Spherical harmonic polynomials; Schrödinger equation for a two-body system; Concluding remarks) -- 4. Dirac equation in higher dimensions (Introduction; Dirac equation in N+1 dimensions; The radial equation; Application to hydrogen atom; Concluding remarks) -- 5. Klein-Gordon equation in higher dimensions (Introduction; The Radial equation; Application to hydrogen atom; Concluding remarks) -- Part III (Application in Non-relativistic Quantum Mechanics) -- 6. Harmonic oscillator (Introduction; Exact solutions of harmonic oscillator; Recurrence relations for the radioal function; Realization of dynamic group SU(1, 1); Generalization to pseudoharmonic ooscillator; Position and momentum information entropy; Conclusions) -- 7. Coulomb potential (Introduction; Exact solution; Shift operators; Mapping between Coulumb and harmonic oscillator radial functions; Realization of dynamic of dynamic group SU (1, 1); Generalization to Kratzer potential; Concluding remarks) -- 8. Wave function ansatz method (Introduction; Sextic potential; Singular one-fraction power potential; Mixture potential; Non-polynomial potential; Screened Coulomb potential; Morse potential; Conclusions) -- 9. Levinson theorem for Schrödinger equation (Introduction; Scattering states and phase shifts; Bound states; Sturm--Liouville theorem; Levinson theorem; Discussions; Conclusions) -- 10. Generalized hypervirial theorem for Schrödinger equation (Introduction; Generalized Blanchard’s and Kramers’ recurrence relations; Applications to central potentials; Conclusions) -- 11. Exact quantization rule and Langer modification (Introduction; WKB approximation; Exact quantization rule; Application to trigonometric Rosen-Morse potential; Proper quantization rule; Illustrations of proper quantization rule; Langer modification in D dimensions; Calculations of logarithmic derivatives of wavefunction; Conclusions) -- 12. Schrödinger equation with position-dependent mass (Introduction; Formalism; Applications to harmonic oscillator and Coulomb potential; Conclusions) -- Part IV (Application in Relativistic Quantum Mechanics) -- 13. Dirac equation with Coulomb potential (Introduction; Exact solutions of hydrogen-like atoms; Analysis of eigenvalues; Generalization to the Dirac equation with Coulomb potential plus scalar potential; Concluding remarks) -- 14. Klein-Gordon equation with Coulomb potential (Introduction; Eigenfunctions and eigenvalues; Analysis of eigenvalues; Generalization: Klein-Gordon equation with Coulomb plus scalar potential; Comparison theorem; Conclusions) -- 15. Levinson theorem for Dirac equation (Introduction; Generalization Sturm-Liouville theorem; Number of bound states; Relativistic Levinson theorem; Discussions; Friedel Theorem; Comparison theorem; Conclusions) -- 16. Generalized hypervirial theorem for Dirac equation (Introduction; Relativistic recurrence relation; Diagonal case; Conclusions) -- 17. Kaluza-Klein theory (Introduction; (4+D) -dimensional Kaluza-Klein theories; Paritcle spectrum of Kaluza-Klein theories for ferminions; Warped extra dimensions; Conclusions) -- PART V (Conclusions and Outlooks) -- 18. Conclusions and outlooks -- Appendices -- References -- Index. |
| 520 ## - SUMMARY, ETC. |
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| Summary, etc |
Higher dimensional theories have attracted much attention because they make it possible to reduce much of physics in a concise, elegant fashion that unifies the two great theories of the 20th century: Quantum Theory and Relativity. This book provides an elementary description of quantum wave equations in higher dimensions at an advanced level so as to put all current mathematical and physical concepts and techniques at the reader’s disposal. A comprehensive description of quantum wave equations in higher dimensions and their broad range of applications in quantum mechanics is provided, which complements the traditional coverage found in the existing quantum mechanics textbooks and gives scientists a fresh outlook on quantum systems in all branches of physics. In Parts I and II the basic properties of the SO(n) group are reviewed and basic theories and techniques related to wave equations in higher dimensions are introduced. Parts III and IV cover important quantum systems in the framework of non-relativistic and relativistic quantum mechanics in terms of the theories presented in Part II. In particular, the Levinson theorem and the generalized hypervirial theorem in higher dimensions, the Schrödinger equation with position-dependent mass and the Kaluza-Klein theory in higher dimensions are investigated. In this context, the dependence of the energy levels on the dimension is shown. Finally, Part V contains conclusions, outlooks and an extensive bibliography. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Physics. |
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| Topical term or geographic name as entry element |
Functional equations. |
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| Topical term or geographic name as entry element |
Quantum theory. |
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| Topical term or geographic name as entry element |
Physics. |
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| Topical term or geographic name as entry element |
Quantum Physics. |
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| Topical term or geographic name as entry element |
Classical and Quantum Gravitation, Relativity Theory. |
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| Topical term or geographic name as entry element |
Difference and Functional Equations. |
| 710 2# - ADDED ENTRY--CORPORATE NAME |
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| Corporate name or jurisdiction name as entry element |
SpringerLink (Online service) |
| 773 0# - HOST ITEM ENTRY |
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| Title |
Springer eBooks |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY |
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| Display text |
Printed edition: |
| International Standard Book Number |
9789400719163 |
| 856 40 - ELECTRONIC LOCATION AND ACCESS |
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| Uniform Resource Identifier |
http://dx.doi.org/10.1007/978-94-007-1917-0 |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) |
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| Source of classification or shelving scheme |
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| Item type |
E-Book |
