## The Radial Equation for *

It is sometimes useful to use

to solve a radial equation problem. We can rewrite the equation for .

This now looks just like the one dimensional equation except the pseudo potential due to angular momentum has been added.

We do get the additional condition that

to keep normalizable.

For the case of a constant potential , we define and , and the radial equation becomes.

For , its easy to see that and are solutions. Dividing by to get , we see that these are and . The solutions can be checked for other , with some work.

Jim Branson 2013-04-22