Advertisement

The Radial Equation for Central Force Fields

  • James B. Seaborn
Part of the Texts in Applied Mathematics book series (TAM, volume 8)

Abstract

We saw in the previous chapter that for spherically symmetric force fields solutions to Schrödinger’s equation are
$$u\left( r \right) = R\left( r \right)Y\left( {\theta ,\phi } \right)$$
where Y(λ, ø) satisfies Eq. (5.9). The general solution can be written as an infinite sum of such products.1 The radial dependence of u(r) is contained in R(r) which is described by the differential equation2
$$\frac{d}{{dr}}\left( {{r^2}\frac{d}{{dr}}R\left( r \right)} \right) + \left\{ {\frac{{2m{r^2}}}{{{h^2}}}\left[ {E - V\left( R \right)} \right] - l(l + 1)} \right\}R(r) = 0$$
(6.1)
The function V(r) represents the potential energy of the particle in the central field.

Keywords

Hypergeometric Function Polynomial Solution Radial Wave Function Radial Equation Spherical Bessel Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer Science+Business Media New York 1991

Authors and Affiliations

  • James B. Seaborn
    • 1
  1. 1.Department of PhysicsUniversity of RichmondUSA

Personalised recommendations