The Weierstrass Elliptic Function and Applications in Classical and Quantum Mechanics : A Primer for Advanced Undergraduates (Springerbriefs in Physics)

Pastras, Georgios

Springer Nature Switzerland AG（2020/11発売）

• 製本 Paperback:紙装版/ペーパーバック版／ページ数 111 p.
• 言語 ENG
• 商品コード 9783030593841

Full Description

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.

Contents

Weierstrass Elliptic Function.- Weierstrass Quasi-periodic Functions.- Real Solutions of Weierstrass Equation.- Applications in Classical Mechanics.- Applications in Quantum Mechanics.- Epilogue and Projects for the Advanced Reader.