Quantum Mechanics and Path Integrals

Fülszöveg

Quantum Mechanics and Path Integrals This book is intended (1) to supplement a first-year course in quantum mechanics; (2) to enable physicists already acquainted with more traditional approaches to quantum mechanics to enlarge their familiarity with this subject; and (3) to provide a source book for the path integrál techniques developed by R. P. Feynman. The approach is primarily intuitive and relies on the so-called "path integrál method" developed originally by the senior author. This method is most powerful when applied to a particular set of quantum mechanical problems, such as the scattering of an electron in a potential field, or various pertubation problems. The authors concentrate on those problems where this approach is most powerful and, while showing the connection between the path integrál approach and the Schroedinger wave equation technique, do not treat those aspects of tiie subject which are best treated by the wave equation method. In this sense, the book is a... Tovább

Fülszöveg

Quantum Mechanics and Path Integrals This book is intended (1) to supplement a first-year course in quantum mechanics; (2) to enable physicists already acquainted with more traditional approaches to quantum mechanics to enlarge their familiarity with this subject; and (3) to provide a source book for the path integrál techniques developed by R. P. Feynman. The approach is primarily intuitive and relies on the so-called "path integrál method" developed originally by the senior author. This method is most powerful when applied to a particular set of quantum mechanical problems, such as the scattering of an electron in a potential field, or various pertubation problems. The authors concentrate on those problems where this approach is most powerful and, while showing the connection between the path integrál approach and the Schroedinger wave equation technique, do not treat those aspects of tiie subject which are best treated by the wave equation method. In this sense, the book is a íupplement to existing texts in quantum mechanics. Highlights 1. Above all, the use of the Feynman path integrál approach, first as a technique for learning about quantum mechanics and then as a technique for solving quantum mechanic problems. The significance is twofold: a. thevisual, diagram-based mathematical concepts help a student to develop a valid intuitive approach which is not based on the old billiard ball picture of atomic particles but rather upon an intuitive appreciation of the actual quantum mechanical properties of small particles. b. It is a powerful tool for solving physics problems which, using older methods, required cumbersome and lengthy calculations. 2. Scattering problems, more difficult when approached by traditional techniques, are treated in an early section since they can
be solved in a comparatively simple manner. 3. The more customary Schroedinger wave equation approach is described and its relationship with the path integrál approach treated in detail. 4. One chapter is devoted to quantum electrodynamics, a topic not usually presented in any detail in first year quantum mechanics texts. 5. The utility of the path integrál approach is alsó shown in attacking problems in statistical mechanics and other classical probability problems. From the Authors' Preface The path integrál approach was used as a technique for teaching quantum mechanics for a tew years at the California Institute of Technology. It was during this period that A. R. Hibbs, a student of Feynman's, began to develop a set of notes suitable for converting a lecture course on the path integrál approach to quantum mechanics into a book on the same subject. Over the succeeding years, as the book itself was elaborated, other subjects were brought into both the lectures of Dr. Feynman and the book; examples are statistical mechanics and the variational principle. At the same time, Dr. Feynman's approach to teaching the subject of quantum mechanics evolved somewhat away from the initial path integrál approach. At the present time, it appears that the operator technique is both deeper and more powerful for the solution of more generál quantum-mechanical problems. Nevertheless, the path integrál approach provides an intuitive appreciation of quantum-mechanical behavior which is extremely valuable in gaining an intuitive appreciation of quantummechanical laws. For this reason, in those fields of quantum-mechanics where the path integrál approach turns out to be particularly useful, most of which are described in this book, the physics student is provided with an excellent grasp of basic quantum-mechanical principles which will permit him to be more effective in solving problems in broader areas of theoretical physics. Vissza