The Weierstrass Elliptic Function and Applications in Classical and Quantum Mechanics
A Primer for Advanced Undergraduates
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Beschreibung
The field of elliptic functions, apart from its own mathematical beauty, has many applications in physics in a variety of topics, such as string theory or integrable systems. This book, which focuses on the Weierstrass theory of elliptic functions, aims at senior undergraduate and junior graduate students in physics or applied mathematics. Supplemented by problems and solutions, it provides a fast, but thorough introduction to the mathematical theory and presents some important applications in classical and quantum mechanics. Elementary applications, such as the simple pendulum, help the readers develop physical intuition on the behavior of the Weierstrass elliptic and related functions, whereas more Interesting and advanced examples, like the n=1 Lamé problem-a periodic potential with an exactly solvable band structure, are also presented.
Written in a language familiar to physicists and applied mathematicians Helps the reader to build intuitive understanding of the behavior of elliptic functions, through applications in physics Includes problems with solutions
Autor*in
Georgios Pastras
Themen in »The Weierstrass Elliptic Function and Applications in Classical and Quantum Mechanics«
elliptic functions in physics Lamé Potential exact solution of simple pendulum exact solution of cubic potential Weierstrass Quasi-periodic Function