Standing-Wave Solutions

  • Roger G. Newton
Part of the Texts and Monographs in Physics book series (TMP)

Abstract

One of the standard solutions of the Schrôdinger equation is defined by means of the Green’s function
$$G_0^P (k,x)\;: = \;\frac{1}{{(2\pi )^3 }}P\;\int_{IR^3 } {dk} ^\prime \frac{{e^{ik' - x} }}{{k^2 - k'^2 }}\; = \; - \frac{{\cos k\left| x \right|}}{{4\pi \left| x \right|}},$$
(5.1)
where P stands for Cauchy’s Principal value, the integral equation
$$\psi ^P (k,\theta ,x) = e^{ik\theta \cdot x} + \int {_{IR^3 } dyG_0^P (k,x - y)V(y)\psi ^P (k,\theta ,y).} $$
(5.2)

Keywords

limE 

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Copyright information

© Springer-Verlag Berlin Heidelberg 1989

Authors and Affiliations

  • Roger G. Newton
    • 1
  1. 1.Department of PhysicsIndiana UniversityBloomingtonUSA

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