The Lippmann–Schwinger Formula and One Dimensional Models with Dirac Delta Interactions

  1. Erman, Fatih
  2. Gadella, Manuel 1
  3. Uncu, Haydar
  1. 1 Universidad de Valladolid
    info

    Universidad de Valladolid

    Valladolid, España

    ROR https://ror.org/01fvbaw18

Libro:
Integrability, Supersymmetry and Coherent States

ISBN: 9783030200862,  9783030200879

Año de publicación: 2019

Páginas: 309-322

Tipo: Capítulo de Libro

DOI: 10.1007/978-3-030-20087-9_13 GOOGLE SCHOLAR lock_openAcceso abierto editor

Resumen

We show how a proper use of the Lippmann–Schwinger equation simplifies the calculations to obtain scattering states for one dimensional systems perturbed by N Dirac delta equations. Here, we consider two situations. In the former, attractive Dirac deltas perturbed the free one dimensional Schrödinger Hamiltonian. We obtain explicit expressions for scattering and Gamow states. For completeness, we show that the method to obtain bound states use comparable formulas, although not based on the Lippmann–Schwinger equation. Then, the attractive N deltas perturbed the one dimensional Salpeter equation. We also obtain explicit expressions for the scattering wave functions. Here, we need regularisation techniques that we implement via heat kernel regularisation.

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