Generalizations to Feynman's Path Integration Methods in One Dimension

TL;DR

This paper reviews and extends Feynman's one-dimensional path integration techniques using variational calculus, broadening their theoretical foundation and potential applications.

Contribution

It introduces generalizations of Feynman's path integration methods based on variational calculus in one dimension, enhancing their theoretical framework.

Findings

Generalized path integration methods using variational calculus.

Simplified demonstration in one dimension.

Potential for broader applications in quantum mechanics.

Abstract

This paper reviews and generalizes Feynman's path integration methods which use time slicing with straight line segments and Fourier sine series. The generalizations are done from variational calculus considerations and in one dimension for simplicity in demonstrating concepts.