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Integral transforms of the quantum mechanical path integral: Hit function and path-averaged potential

James P. Edwards1,*, Urs Gerber1,2,†, Christian Schubert1,‡, Maria Anabel Trejo1,3,§, and Axel Weber1,∥

  • 1Instituto de Física y Matemáticas, Universidad Michoacana de San Nicolás de Hidalgo, Edificio C-3, Apdo. Postal 2-82, C.P. 58040, Morelia, Michoacán, Mexico
  • 2Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de Mexico, A.P. 70-543, C.P. 04510 Ciudad de México, Mexico
  • 3Theoretisch-Physikalisches Institut, Friedrich-Schiller-Universität Jena, Max-Wien-Platz 1, 07743 Jena, Germany

  • *Corresponding author: jedwards@ifm.umich.mx
  • †gerber@correo.nucleares.unam.mx
  • ‡schubert@ifm.umich.mx
  • §mtrejo@ifm.umich.mx
  • ∥axel@ifm.umich.mx
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Phys. Rev. E 97, 042114 – Published 10 April, 2018

DOI: https://doi.org/10.1103/PhysRevE.97.042114

Abstract

We introduce two integral transforms of the quantum mechanical transition kernel that represent physical information about the path integral. These transforms can be interpreted as probability distributions on particle trajectories measuring respectively the relative contribution to the path integral from paths crossing a given spatial point (the hit function) and the likelihood of values of the line integral of the potential along a path in the ensemble (the path-averaged potential).

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Phys. Rev. E 97, 042114– Published 10 April, 2018
  • Received 25 October 2017
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