From Classical to Quantum Mechanics: An Introduction to the Formalism, Foundations and Applications

by Giampiero Esposito , Giuseppe Marmo , George Sudarshan

• ISBN13: 9780521833240
• ISBN10: 0521833248
• Format: Hardcover
• Copyright: 2004-04-19
• Publisher: Cambridge University Press

Summary

This textbook provides a pedagogical introduction to the formalism, foundations and applications of quantum mechanics. Part I covers the basic material which is necessary to understand 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, Helmholtz equation and eikonal approximation, introduction to spin, perturbation theory and scattering theory. The Weyl quantization is presented in Part II, along with the postulates of quantum mechanics. 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 aid the reader's understanding.

Table of Contents

Preface

Acknowledgements

Part I. From Classical to Wave Mechanics: 1. Experimental foundations of quantum theory

2. Classical dynamics

3. Wave equations

4. Wave mechanics

5. Applications of wave mechanics

6. Introduction to spin

7. Perturbation theory

8. Scattering theory

Part II. Weyl Quantization and Algebraic Methods: 9. Weyl quantization

10. Harmonic oscillators and quantum optics

11. Angular momentum operators

12. Algebraic methods for eigenvalue problems

13. From density matrix to geometric phases

Part III. Selected Topics: 14. From classical to quantum statistical mechanics

15. Lagrangian and phase-space formulations

16. Dirac equation and no-interaction theorem

References

Index.