Feynman’s Path Integral explained with basic Calculus

Richard P. Feynman shared the story of discovering the Path Integral in his Nobel Lecture. He had learned of a paper by Paul Dirac at a beer party from a gentleman named Jehle. Pouring over the same together at a library the day next, to Jehle’s utter astonishment, Feynman derived Schrodinger’s equation in real-time based on an idea from that paper. The key concept in that derivation was the “propagator”, which gave birth to the field of “Feynman’s Path Integral.” You will learn exactly how Feynman did it, in this book.

The Path Integral is a formulation of quantum mechanics describing both non-relativistic (low speed) and relativistic (high speed) quantum phenomena, including quantum electrodynamics, and other quantum field theories. It is usually considered an advanced topic reserved for graduate-level courses. This book presents Path Integrals for non-relativistic particles from first principles with no more than basic Calculus. With minimal prerequisites, the presentation in this book hopes to make Path Integrals accessible without advanced training.

What this book will do for you…

• Learn how Path Integrals appear in Quantum Mechanics via Propagators.
• Learn how the classical trajectory of a particle is connected to the “quantum” propagator.
• Calculate the Propagator for a Free Particle à Use it to Derive:
  • de Broglie’s Wavelength.
  • Einstein’s Energy-Frequency Relationship.
• Calculate the Propagator for a Particle with Potential and Kinetic Energy.
• Derive Schrodinger’s Equation using the Propagator.

Inside the Book:

1. Learn Feynman’s Path Integral technique with basic Calculus.
2. 7 chapters, starting from a review of Mathematical Prerequisites.
3. Presentation interspersed with Exercises and Worked-out Solutions to consolidate your learning.

About the author:

Swapnonil Banerjee has a Ph.D. in Physics from the University of California, Davis, and many years of teaching experience from K12 to university physics courses. He is passionate about simplifying complex ideas, which served as a primary motivation for writing this book.

Swapnonil has extensive research experience in theoretical physics. He made important contributions to the study of a new material called semi-Dirac, in which electrons behave as non-relativistic, massive particles or effectively relativistic, massless particles depending on the direction of their movement. In one direction, the electron’s energy-momentum relationship is indicative of the electron’s having a definitive mass; in the orthogonal direction, the electron’s energy-momentum relationship indicates a surprising absence of mass.

Swapnonil has also contributed to biotechnology, co-developing the Poisson Plus algorithm used for estimating the concentration of biomolecules via the digital PCR technique, and holds a patent for this work.

Swapnonil has published in reputed journals including Nature Scientific Reports and Physical Review Letters.

Swapnonil’s interests besides research and teaching include people and culture. He co-authored the historical fiction Deflected, a fast-paced, wartime romance based on the life of the nineteenth-century mathematician who calculated the height of Mount Everest and established it as the highest point on Earth.

Email swapno.banerjee@gmail.com

Connect: https://www.linkedin.com/in/swapnonil-banerjee-phd-5597553b/