The Weierstrass Elliptic Function and Applications in Classical and Quantum Mechanics

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.

Autorentext

Dr. Georgios Pastras was born in Patras, Greece. He received his BS in Physics from University of Patras in 2002 and he obtained his PhD in Physics from Harvard University in 2009. He has worked as a post-doctoral scientific collaborator in École Polytechnique Fédérale de Lausanne, University of Patras, National Technical University of Athens and he is currently the principal investigator of the research project "HAPPEN" at the Institute of Nuclear and Particle Physics in the National Center for Scientific Research "Demokritos", which is funded by the Hellenic Foundation for Research and Innovation and investigates the connection between gravity and quantum entanglement.

He has conducted research on a variety of topics in theoretical high energy physics including spontaneous metastable supersymmetry breaking, black hole thermodynamics in higher derivative gravity, tunneling solutions in quantum field theory, entanglement in quantum field theories, holographic entanglement entropy, Pohlmeyer reduction and classical string solutions. Between 2012 and 2014, he had a side-career in engineering, focusing on energy efficiency of manufacturing processes, modelling of non-conventional manufacturing processes and robotics.

Dr. Georgios Pastras has taught in Harvard University for nine semesters as a teaching fellow; He has received the "Certificate of distinction in teaching" by the Derek Bok Center for Teaching and Learning twice and he has been awarded with the "Harold T. White Prize for Excellence in the Teaching of Physics" by the Harvard University Physics Department.

Inhalt
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.