This book provides an ideal introduction to the use of Feynman path integrals in the fields of quantum mechanics and statistical physics. It is written for graduate students and researchers in physics, mathematical physics, applied mathematics as well as chemistry. The material is presented in an accessible manner for readers with little knowledge of quantum mechanics and no prior exposure to path integrals. It begins with elementary concepts and a review of quantum mechanics that gradually builds the framework for the Feynman path integrals and how they are applied to problems in quantum mechanics and statistical physics. Problem sets throughout the book allow readers to test their understanding and reinforce the explanations of the theory in real situations.
- Comprehensive and rigorous yet, presents an easy-to-understand approach.
- Applicable to a wide range of disciplines.
- Accessible to those with little, or basic, mathematical understanding.
Table of Contents
1 Path Integral Formalism Intuitive Approach
2 Matrix Representation of Linear Operators
3 Operators in Phase Space
4 Transition Amplitude
5 Stationary and Quasi-Classical Approximations
6 Gaussian Functional Integrals
7 From Path Integration to the Schrödinger Equation
8 Quasi-Classical Approximation
9 Free Particle and Harmonic Oscillator
10 Matrix Element of a Physical Operator via Functional Integral
11 Path Integral Perturbation Theory
12 Transition Matrix Element
13 Functional Derivative
14 Quantum Statistical Mechanics Functional Integral Approach
15 Partition Function and Density Matrix Path Integral Representation
16 Quasi-Classical Approximation in Quantum Statistical Mechanics
17 Feynman Variational Method
18 Polaron Theory
19 Multi-Photon Absorption by Polarons in a Spherical Quantum Dot
20 Polaronic Kinetics in a Spherical Quantum Dot
21 Kinetic Theory of Gases
Lukong Cornelius Fai is professor of theoretical physics at the Department of Physics, Faculty of Sciences, University of Dschang. He is Head of Condensed Matter and Nanomaterials as well as Mesoscopic and Multilayer Structures Laboratory. He was formerly a senior associate at the Abdus Salam International Centre for Theoretical Physics (ICTP), Italy. He holds a Masters of Science in Physics and Mathematics (June 1991) as well as a Doctor of Science in Physics and Mathematics (February 1997) from Moldova State University. He is an author of over a hundred scientific publications and three textbooks