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Author:   Shi-Hai Dong
Publisher:   Springer
Imprint:   Springer
Edition:   2011 ed.
Dimensions:   Width: 15.50cm , Height: 1.70cm , Length: 23.50cm
Weight:   0.498kg
ISBN:  

9789401782302

ISBN 10:   940178230
Pages:   295
Publication Date:   21 November 2014
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   Manufactured on demand  
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Table of Contents

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.

Reviews

Wave Equations in Higher Dimensions is a well-written, comprehensive and self-contained book which is designed for graduate students and researchers in physics and mathematics. ... The author succeeds in fluently presenting the necessary and important material on the subject. (Dogan Demirhan, Mathematical Reviews, June, 2017) Wave Equations in Higher Dimensions is a well-written, comprehensive and self-contained book which is designed for graduate students and researchers in physics and mathematics. ... The author succeeds in fluently presenting the necessary and important material on the subject. (Dogan Demirhan, Mathematical Reviews, June, 2017)

“Wave Equations in Higher Dimensions is a well-written, comprehensive and self-contained book which is designed for graduate students and researchers in physics and mathematics. … The author succeeds in fluently presenting the necessary and important material on the subject.” (Dogan Demirhan, Mathematical Reviews, June, 2017) “Wave Equations in Higher Dimensions is a well-written, comprehensive and self-contained book which is designed for graduate students and researchers in physics and mathematics. … The author succeeds in fluently presenting the necessary and important material on the subject.” (Dogan Demirhan, Mathematical Reviews, June, 2017)

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