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World Scientific lecture notes in physics

Trajectories and Rays: The Path-Summation in Quantum Mechanics and Optics I

Anedio Ranfagni, Daniela Mugnai, P Moretti, Maurizio Cetica

Published Dec 1, 1990• 7 citations
Publisher
DOI
10.1142/0760

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This book presents selected topics about the path-integral method in Quantum Mechanics and Optics. Starting from an introduction to the grounds of functional integration theory, the main arguments of quantum and statistical mechanics, where the path-integral method works, are exposed. In particular, the partition function, the concept of instanton, tunneling and dissipative phenomena are analysed. The final section is devoted to selected and solved problems. This volume will be useful to beginners as well as more advanced students and researchers in the field.
Classical ray and wave optics share a common structure with quantum mechanics. Much of this results from the representations given to abstract operators. It is possible to build a mathematical bridge that allows one to transform back and forth between the ray and wave picture. This is given by the Feynman path integral representation. The map between the ray and wave description is given in terms of a sum over histories integration. In particular, it allows for the computation of wave phenomena by the summation of multiple ray paths of a phase function connected to the classical optical path length.