Feynman's Thesis : A New Approach to Quantum Theory

by Brown, Laurie M.; Feynman, Richard Phillips

• ISBN13: 9789812563668
• ISBN10: 9812563660
• Format: Hardcover
• Copyright: 2005-10-30
• Publisher: World Scientific Pub Co Inc

Summary

Richard Feynman's never previously published doctoral thesis formed the heart of much of his brilliant and profound work in theoretical physics. Entitled ?The Principle of Least Action in Quantum Mechanics, ? its original motive was to quantize the classical action-at-a-distance electrodynamics. Because that theory adopted an overall space?time viewpoint, the classical Hamiltonian approach used in the conventional formulations of quantum theory could not be used, so Feynman turned to the Lagrangian function and the principle of least action as his points of departure. The result was the path integral approach, which satisfied ? and transcended ? its original motivation, and has enjoyed great success in renormalized quantum field theory, including the derivation of the ubiquitous Feynman diagrams for elementary particles. Path integrals have many other applications, including atomic, molecular, and nuclear scattering, statistical mechanics, quantum liquids and solids, Brownian motion, a

Table of Contents

Preface	vii
The Principle of Least Action in Quantum Mechanics
R. P. Feynman
Introduction	1	(5)
Least Action in Classical Mechanics	6	(18)
The Concept of Functional	6	(3)
The Principle of Least Action	9	(1)
Conservation of Energy. Constants of the Motion	10	(6)
Particles Interacting through an Intermediate Oscillator	16	(8)
Least Action in Quantum Mechanics	24	(47)
The Lagrangian in Quantum Mechanics	26	(6)
The Calculation of Matrix Elements in the Language of a Lagrangian	32	(2)
The Equations of Motion in Lagrangian Form	34	(5)
Translation to the Ordinary Notation of Quantum Mechanics	39	(2)
The Generalization to Any Action Function	41	(1)
Conservation of Energy. Constants of the Motion	42	(2)
The Role of the Wave Function	44	(2)
Transition Probabilities	46	(3)
Expectation Values for Observables	49	(6)
Application to the Forced Harmonic Oscillator	55	(6)
Particles Interacting through an Intermediate Oscillator	61	(7)
Conclusion	68	(3)
Space-time Approach to Non-Relativistic Quantum Mechanics	71	(40)
R. P. Feynman
The Lagrangian in Quantum Mechanics	111
P. A. M. Dirac