2008/04/15 by James M. Yearsley, James M Yearsley · 1 citation
Mathematics · Physics and Astronomy · #Brownian motion #Dirac delta function #Mathematical functions and polynomials #Path (computing) #Path integral formulation #Propagator #Random Matrices and Applications #Series expansion #quant-ph #stochastic dynamics and bifurcation
paper · pdf · doi:10.1088/1751-8113/41/28/285301
published as J. Phys. A 41, 285301 (2008) · 11 pages, 3 figures
arxiv created 2008/04/15 · openalex publication_date 2008/06/17 · arxiv updated 2012/02/10 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We present a derivation of the propagator for a particle in the presence of the step and delta function potentials. These propagators are known, but we present a direct path integral derivation, based on the path decomposition expansion and the Brownian motion definition of the path integral. The derivation exploits properties of the Catalan numbers, which enumerate certain classes of lattice paths.