ePub The Feynman Path Integral ePub

by Kirk Boyle

The aim of this book is to derive the Feynman Path Integral from first principles and apply it to a simple system, before demonstrating its equivalence to the Schrodinger formulation of quantum mechanics. The necessary prerequisite knowledge makes it suitable for undergraduate or graduate level physicists. Each step is detailed and every calculation is performed explicitly, so they may be followed with ease. Many of the detailed calculations are also hand-written to avoid any ambiguity associated with technical formatting. Chapter 1 gives an introduction to the Feynman Path Integral and the reason for its use. Chapter 2 then summarises the relevant quantum mechanics, including using the operator method to calculate the energy states for the simple harmonic oscillator. Chapter 3 introduces the action functional for an elementary system before Lagrangian and Hamiltonian mechanics are explained in Chapter 4, including canonical transformations and generating functions. The Feynman Path Integral is then derived in Chapter 5, with calculation of the transition amplitude for a particle to move between two fixed points in a given time. Chapter 6 then applies the Feynman Path Integral to the forced harmonic oscillator. In Chapter 7, we apply the path integral to a discrete, Euclidean time action and then in Chapter 8, use the path integral to calculate the ground and successive state energies for the simple harmonic oscillator. In Chapter 9, the general equivalence of the Path Integral and Schrodinger formulations of quantum mechanics are demonstrated. Finally, in Chapter 10, there is a short narrative on the application to Quantum Electrodynamics and Quantum Field Theory in general.

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