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Hyperspherical Harmonics And Their Physical Applications

By: James Emil Avery, John Scales Avery

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eBook | 27 November 2017

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Hyperspherical harmonics are extremely useful in nuclear physics and reactive scattering theory. However, their use has been confined to specialists with very strong backgrounds in mathematics. This book aims to change the theory of hyperspherical harmonics from an esoteric field, mastered by specialists, into an easily-used tool with a place in the working kit of all theoretical physicists, theoretical chemists and mathematicians. The theory presented here is accessible without the knowledge of Lie-groups and representation theory, and can be understood with an ordinary knowledge of calculus. The book is accompanied by programs and exercises designed for teaching and practical use.

Contents:

Preface
Harmonic Functions
Generalized Angular Momentum
Gegenbauer Polynomials
Fourier Transforms in d Dimensions
Fock's Treatment of Hydrogenlike Atoms and Its Generalization
D-Dimensional Hydrogenlike Orbitals in Direct Space
Generalized Sturmians
Choosing Appropriate Hyperspherical Representations
Molecular Integrals from Hyperspherical Harmonics
Lagrangians for Particles and Fields
Coordinate Transformations for N Bodies
Some Illustrative Examples
Appendices:
- The D-Dimensional Harmonic Oscillator
- Molecular Integrals for Slatertype Orbitals
Bibliography
Index

Readership:Scientists and researchers in theoretical physics, theoretical chemistry, and mathematics.
Keywords:Harmonic Functions;Reactive Scattering Theory; Nuclear Physics;Gegenbauer Polynomials;Generalized Sturmians;Slatertype OrbitalsReview:Key Features: