"The Principle of Least Action originates in the idea that, if Nature has a purpose, it should follow a minimum or critical path. This simple principle (and its variants and generalizations) applies to optics, mechanics, electromagnetism, relativity and quantum mechanics, and provides an essential guide to understanding the beauty of physics. This unique text provides an accessible introduction to the action principle across these various fields of physics and examines its history and fundamental role in science"--
"The Principle of Least Action originates in the idea that, if Nature has a purpose, it should follow a minimum or critical path. This simple principle (and its variants and generalizations) applies to optics, mechanics, electromagnetism, relativity and quantum mechanics, and provides an essential guide to understanding the beauty of physics. This unique text provides an accessible introduction to the action principle across these various fields of physics and examines its history and fundamental role in science"--
Alberto Rojo is Associate Professor at Oakland University, Michigan. He is a Fulbright specialist in Physics Education and was awarded the Jack Williams Endowed Chair in Science and Humanities from the University of Eastern New Mexico. His research focuses primarily on theoretical condensed matter and he has previously published books in the popular science field.
Inhaltsangabe
1. Introduction 2. Prehistory of variational principles 3. An excursio to Newton's Principia 4. The optical-mechanical analogy, part I 5. D'Alembert, Lagrange, and the statics-dynamics analogy 6. The optical mechanical analogy, part II: the Hamilton-Jacobi equation 7. Relativity and least action 8. The road to quantum mechanics Appendix A. Newton's solid of least resistance using calculus Appendix B. Original statement of D'Alembert's principle Appendix C. Equations of motion of MacCullagh's ether Appendix D. Characteristic function for a parabolic Keplerian orbit Appendix E. Saddle paths for reections on a mirror Appendix F. Kinetic caustics from quantum motion in one dimension Appendix G. Einstein's proof of the covariance of Maxwell's equations Appendix H. Relativistic four vector potential Appendix I. Ehrenfest's proof of the adiabatic theorem References Index.
1. Introduction 2. Prehistory of variational principles 3. An excursio to Newton's Principia 4. The optical-mechanical analogy, part I 5. D'Alembert, Lagrange, and the statics-dynamics analogy 6. The optical mechanical analogy, part II: the Hamilton-Jacobi equation 7. Relativity and least action 8. The road to quantum mechanics Appendix A. Newton's solid of least resistance using calculus Appendix B. Original statement of D'Alembert's principle Appendix C. Equations of motion of MacCullagh's ether Appendix D. Characteristic function for a parabolic Keplerian orbit Appendix E. Saddle paths for reections on a mirror Appendix F. Kinetic caustics from quantum motion in one dimension Appendix G. Einstein's proof of the covariance of Maxwell's equations Appendix H. Relativistic four vector potential Appendix I. Ehrenfest's proof of the adiabatic theorem References Index.
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