# The Radial Equation for Central Force Fields

Chapter

## Abstract

We saw in the previous chapter that for spherically symmetric force fields solutions to Schrödinger’s equation are
where The function V(

$$u\left( r \right) = R\left( r \right)Y\left( {\theta ,\phi } \right)$$

*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 equation^{2}$$\frac{d}{{dr}}\left( {{r^2}\frac{d}{{dr}}R\left( r \right)} \right) + \left\{ {\frac{{2m{r^2}}}{{{h^2}}}\left[ {E - V\left( R \right)} \right] - l(l + 1)} \right\}R(r) = 0$$

(6.1)

*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.

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## Copyright information

© Springer Science+Business Media New York 1991