dissertation · Zenodo (CERN European Organization for Nuclear Research) · 2025

Path integral formulation of quantum mechanics

Dey, Arpan

Cited by 0Open access

Abstract

In this article, we present a rigorous introduction to Feynman’s path integral formulation of quantum mechanics. We start by outlining the motivation behind the path integral formulation of quantum mechanics. Then we build the mathematics required for defining the sum-over-paths and derive the free particle propagator, as well as the propagator for a particle with a non-zero potential energy, with particular focus on linear and quadratic potential energies. We use these results to arrive at some standard results in quantum physics using path integrals: namely Planck-Einstein equation, de-Broglie equation and Schrödinger equation. This helps us appreciate the equivalence between the path integral and the canonical formulation, as well as understand the difference in the approaches employed by the two formulations to arrive at the results. We also use Python to generate plots of the free particle wave function and propagator as functions of position and time, and explore the conceptual difference between the wave function in canonical quantum mechanics and the propagator used in the path integral formulation. We also introduce the basic idea behind perturbation theory, by using the free particle propagator to study a particle that moves between two potential-free points in spacetime, but via intermediate points with non-zero potentials, in one of the appendices. In the end, we discuss path integrals in a broad perspective, and make some general comments on the future of theoretical physics.

Cite this paper

APA 7

Dey, A. (2025). Path integral formulation of quantum mechanics. Zenodo (CERN European Organization for Nuclear Research). https://doi.org/10.5281/zenodo.15125184

MLA 9

Dey, Arpan. “Path integral formulation of quantum mechanics.” Zenodo (CERN European Organization for Nuclear Research), 2025, https://doi.org/10.5281/zenodo.15125184.

Chicago

Dey, Arpan. 2025. “Path integral formulation of quantum mechanics.” Zenodo (CERN European Organization for Nuclear Research). https://doi.org/10.5281/zenodo.15125184.

Harvard

Dey, A. (2025) ‘Path integral formulation of quantum mechanics’, Zenodo (CERN European Organization for Nuclear Research). Available at: https://doi.org/10.5281/zenodo.15125184.

BibTeX

@phdthesis{dey2025path,
  title = {{Path integral formulation of quantum mechanics}},
  author = {Dey, Arpan},
  school = {Zenodo (CERN European Organization for Nuclear Research)},
  year = {2025},
  doi = {10.5281/zenodo.15125184}
}

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