Elements of Hamiltonian Mechanics and Electromagnetism

Chapter
Part of the UNITEXT for Physics book series (UNITEXTPH)

Abstract

We recall some basic notions of Classical Physics useful to understand the birth and the formulation of Quantum Mechanics. We introduce Hamilton’s equations of motion and discuss the main properties of Poisson brackets, canonical transformations, Hamilton–Jacobi method, and separation of variables. We study Liouville’s equation and its relation with the evolution laws of states and observables. The laws of Geometrical Optics are formulated via Fermat’s principle and the analogy with Classical Mechanics is discussed. Concerning Electromagnetism, we recall Maxwell’s equations and describe some properties of the electromagnetic field in vacuum and in inhomogeneous media. In particular, we discuss the short wavelength limit of Wave Optics. The chapter is intended as a short review, some topics are discussed using only heuristic arguments and there is no pretense of completeness.

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Dipartimento di Matematica Guido CastelnuovoUniversità degli Studi di Roma “La Sapienza”RomeItaly

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