Calculus and Mechanics on Two-Point Homogenous Riemannian Spaces (Lecture Notes in Physics) [Hardcover]

Alexey V. Shchepetilov (Author)

Book Description

Publication Date: October 9, 2006 | ISBN-10: 3540353844 | ISBN-13: 978-3540353843 | Edition: 1

This is an introduction to classical and quantum mechanics on two-point homogenous Riemannian spaces, empahsizing spaces with constant curvature. Chapters 1-4 provide basic notations for studying two-body dynamics. Chapter 5 deals with the problem of finding explicitly invariant expressions for the two-body quantum Hamiltonian. Chapter 6 addresses one-body problems in a central potential. Chapter 7 investigates the classical counterpart of the quantum system introduced in Chapter 5. Chapter 8 discusses applications in the quantum realm.

Editorial Reviews

Review

From the reviews:

"This book has eight chapters and a bibliography list containing 215 references. It is written in a clear and straightforward way that makes it useful even for nonspecialists in the field. … In particular, the book contains interesting discussions of applications of the Poincaré section method to some problems in constant curvature spaces. … The book is a valuable complete source for many-body problems on two-point homogeneous spaces." (Alexei Tsygvintsev, Mathematical Reviews, Issue 2008 f)

From the Back Cover

The present monograph gives a short and concise introduction to classical and quantum mechanics on two-point homogenous Riemannian spaces, with empahsis on spaces with constant curvature. Chapter 1-4 provide the basic notations from differential geometry for studying two-body dynamics in these spaces. Chapter 5 deals with the problem of finding explicitly invariant expressions for the two-body quantum Hamiltonian. Chapter 6 addresses one-body problems in a central potential. Chapter 7 studies the classical counterpart of the quantum system of chapter 5. Chapter 8 investigates some applications in the quantum realm, namely for the coulomb and oscillator potentials.

Product Details

• Hardcover: 274 pages
• Publisher: Springer; 1 edition (October 9, 2006)
• Language: English
• ISBN-10: 3540353844
• ISBN-13: 978-3540353843
• Product Dimensions: 9.3 x 6.1 x 0.8 inches
• Shipping Weight: 1.2 pounds (View shipping rates and policies)
• Amazon Best Sellers Rank: #7,337,714 in Books (See Top 100 in Books)

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