An Introduction into the Feynman Path Integral

TL;DR

This paper introduces the Feynman path integral in quantum mechanics, covering its formulation in Riemann spaces, space-time transformations, and applications to harmonic oscillators and Coulomb potential.

Contribution

It provides a concise overview of the Feynman path integral theory, including its mathematical formulation and key applications in quantum systems.

Findings

Path integral formulated in Riemann spaces using Weyl ordering

Application to harmonic oscillator and Coulomb potential

Outline of space-time transformations and variable separation

Abstract

In this lecture a short introduction is given into the theory of the Feynman path integral in quantum mechanics. The general formulation in Riemann spaces will be given based on the Weyl- ordering prescription, respectively product ordering prescription, in the quantum Hamiltonian. Also, the theory of space-time transformations and separation of variables will be outlined. As elementary examples I discuss the usual harmonic oscillator, the radial harmonic oscillator, and the Coulomb potential. Lecture given at the graduate college ''Quantenfeldtheorie und deren Anwendung in der Elementarteilchen- und Festk\"orperphysik'', Universit\"at Leipzig, 16-26 November 1992.