Feynman Path Integrals in Quantum Mechanics and Statistical Physics
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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.
Table of Contents
Chapter 1. Path Integral Formalism Intuitive Approach.
Chapter 2. Matrix Representation of Linear Operators.
Chapter 3. Operators in Phase Space.
Chapter 4. Transition Amplitude.
Chapter 5. Stationary and Quasi-Classical Approximations.
Chapter 6. Generalized Feynman Path Integration.
Chapter 7. From Path Integration to the Schödinger Equation.
Chapter 8. Quasi-Classical Approximation.
Chapter 9. Free Particle and Harmonic Oscillator.
Chapter 10. Matrix Element of a Physical Operator via Functional Integral.
Chapter 11. Path Integral Perturbation Theory.
Chapter 12. Transition Matrix Element.
Chapter 13. Functional Derivative.
Chapter 14. Quantum Statistical Mechanics Functional Integartion Approach.
Chapter 15. Partition Function and Density Matrix Path Integration Representation.
Chapter 16. Quasi-Classical Approximation in Quantum Statistical Mechanics.
Chapter 17. Feynman Variational Method.
Chapter 18. Polaron Theory.
Chapter 19. Multiphoton Absorption by Polarons in a Spherical Quantum Dot.
Chapter 20. Polaronic Kinetics in a Speherical Quantum Dot.
Chapter 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