Feynman Path Integrals in Quantum Mechanics and Statistical Physics

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.

Features:

• 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.

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