# WKB in Spherical Coordinates

### From FSUPhysicsWiki

It is possible to apply the WKB approximation to the radial equation using a method by R. E. Langer (1937).

Recall that

and that satisfies the effective one-dimensional Schrödinger equation,

We now perform the following transformations:

Note that, for The radial equation becomes

In this case, the Bohr-Sommerfeld quantization rule is as in the purely one-dimensional case, but with an effective potential,

## Problem

Use the WKB approximation to estimate the energy spectrum for a Hydrogen atom.

*Hint*: Use the relation,

where

and and are the classical turning points of the (effective) potential appearing in the WKB approximation for this problem, and the integral,