VARIATIONAL PRINCIPLES IN DYNAMICS AND QUANTUM THEORY

Focusing on applications most relevant to modern physics, this text surveys variational principles and examines their relationship to dynamics and quantum theory. It stresses the history and theory of these mathematical concepts rather than their mechanics, providing many insights into the development of quantum mechanics in a remarkably lucid, compact form. Professional physicists and mathematicians, as well as advanced students with a strong mathematical background, will find it highly stimulating. After summarizing the historical background from Pythagoras to Francis Bacon, the text covers Fermat's principle of least time, the principle of least action of Maupertuis, the development of this principle by Euler and Lagrange, and the equations of Lagrange and Hamilton. After this general treatment of variational principles, the authors proceed to derive Hamilton's principle, the Hamilton-Jacobi equation, and Hamilton's canonical equations. An investigation of electrodynamics in Hamiltonian form follows, along with an overview of variational principles in classical dynamics. The text then analyzes its most significant topics: the relation between variational principles and wave mechanics, and the principles of Feynman and Schwinger in quantum mechanics. Two concluding chapters extend the discussion to hydrodynamics and natural philosophy.