Phys. Rev. A 37, 973–976 (1988)Green’s function and propagator for the one-dimensional δ-function potentialReceived 2 July 1987; published in the issue dated February 1988 A particle in a one-dimensional δ-function potential possesses both discrete and continuum solutions. The configuration-space Green’s function and propagator for this problem are derived by explicit summation over the spectrum of eigenstates. The momentum-space Green’s function is also obtained. The propagator does not contain the classical action function in any simple way, in contrast to the usual structure in Feynman’s path-integral formalism. Various analogies between the δ-function and Coulomb problems are discussed. © 1988 The American Physical Society URL:
http://link.aps.org/doi/10.1103/PhysRevA.37.973
DOI:
10.1103/PhysRevA.37.973
PACS:
03.65.-w
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