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An Introductory Guide to Computational Methods for the Solution of Physics Problems pp 63–76Cite as

The Integral Equation Corresponding to a Differential Equation

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Abstract

In this chapter we present an integral equation, whose solution is the same as that of a corresponding second order differential equation. We discuss the advantages of working with the integral equation, called Lippmann–Schwinger (L–S). We show how a numerical solution of such an equation can be obtained by expanding the wave function in terms of Chebyshev polynomials, and give an example for a simple one-dimensional Schrödinger equation. This method is denoted as S-IEM (for spectral integral equation method), and its accuracy is discussed. A case of a shape resonance is also presented, and the corresponding behavior of the wave functions for different incident energies is described.

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Author information

Authors and Affiliations

  1. University of Connecticut, Storrs, CT, USA

    George Rawitscher

  2. H4D Scientific Research Laboratory, Bela Vista, São Paulo, Brazil

    Victo dos Santos Filho

  3. Federal Institute of Sergipe (IFS), Nossa Senhora da Glória, Sergipe, Brazil

    Thiago Carvalho Peixoto

Authors
  1. George Rawitscher
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  2. Victo dos Santos Filho
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  3. Thiago Carvalho Peixoto
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Corresponding author

Correspondence to Victo dos Santos Filho .

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Rawitscher, G., dos Santos Filho, V., Peixoto, T.C. (2018). The Integral Equation Corresponding to a Differential Equation. In: An Introductory Guide to Computational Methods for the Solution of Physics Problems. Springer, Cham. https://doi.org/10.1007/978-3-319-42703-4_6

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