From Classical To Quantum Mechanics

From Classical to Quantum Mechanics This book provides a pedagogical introduction to the formalism, foundations and applications of quantum mechanics. Part I covers the basic material that is necessary to an understanding of the transition from classical to wave mechanics. Topics include classical dynamics, with emphasis on canonical transformations and the Hamilton–Jacobi equation; the Cauchy problem for the wave equation, the Helmholtz equation and eikonal approximation; and introductions to spin, perturbation theory and scattering theory. The Weyl quantization is presented in Part II, along with the postulates of quantum mechanics. The Weyl programme provides a geometric framework for a rigorous formulation of canonical quantization, as well as powerful tools for the analysis of problems of current interest in quantum physics. In the chapters devoted to harmonic oscillators and angular momentum operators, the emphasis is on algebraic and group-theoretical methods. Quantum entanglement, hidden-variable theories and the Bell inequalities are also discussed. Part III is devoted to topics such as statistical mechanics and black-body radiation, Lagrangian and phase-space formulations of quantum mechanics, and the Dirac equation. This book is intended for use as a textbook for beginning graduate and advanced undergraduate courses. It is self-contained and includes problems to advance the reader’s understanding. Giampiero Esposito received his PhD from the University of Cambridge in 1991 and has been INFN Research Fellow at Naples University since November 1993. His research is devoted to gravitational physics and quantum theory. His main contributions are to the boundary conditions in quantum field theory and quantum gravity via functional integrals. Giuseppe Marmo has been Professor of Theoretical Physics at Naples University since 1986, where he is teaching the first undergraduate course in quantum mechanics. His research interests are in the geometry of classical and quantum dynamical systems, deformation quantization, algebraic structures in physics, and constrained and integrable systems. George Sudarshan has been Professor of Physics at the Department of Physics of the University of Texas at Austin since 1969. His research has revolutionized the understanding of classical and quantum dynamics. He has been nominated for the Nobel Prize six times and has received many awards, including the Bose Medal in 1977. i ii FROM CLASSICAL TO QUANTUM MECHANICS An Introduction to the Formalism, Foundations and Applications Giampiero Esposito, Giuseppe Marmo INFN, Sezione di Napoli and Dipartimento di Scienze Fisiche, Universit` a Federico II di Napoli George Sudarshan Department of Physics, University of Texas, Austin iii    Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo Cambridge University Press The Edinburgh Building, Cambridge  , UK Published in the United States of America by Cambridge University Press, New York www.cambridge.org Information on this title: www.cambridge.org/9780521833240 © G. Esposito, G. Marmo and E. C. G. Sudarshan 2004 This publication is in copyright. Subject to statutory exception and to the provision of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press. First published in print format 2004 - - ---- eBook (NetLibrary) --- eBook (NetLibrary) - - ---- hardback --- hardback Cambridge University Press has no responsibility for the persistence or accuracy of s for external or third-party internet websites referred to in this publication, and does not guarantee that any content on such websites is, or will remai