The Radial Equation for Central Force Fields

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


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
$$\frac{d}{{dr}}\left( {{r^2}\frac{d}{{dr}}R\left( r \right)} \right) + \left\{ {\frac{{2m{r^2}}}{{{h^2}}}\left[ {E - V\left( R \right)} \right] - l(l + 1)} \right\}R(r) = 0$$
The function V(r) represents the potential energy of the particle in the central field.


Hypergeometric Function Polynomial Solution Radial Wave Function Radial Equation Spherical Bessel Function 
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Copyright information

© Springer Science+Business Media New York 1991

Authors and Affiliations

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

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