For the common
problem of central potentials
,
we use the obvious **rotational symmetry** to find that the **angular momentum**,
, operators commute with
,

but they do not commute with each other.

We want to find

We chose our two operators to be and .

Some computation reveals that we can write

With this the kinetic energy part of our equation will only have derivatives in assuming that we have eigenstates of .

The

will be a solution. The will be eigenfunctions of

so the radial equation becomes

We must come back to this equation for each which we want to solve.

We **solve the angular part of the problem in general**
using angular momentum operators.
We find that **angular momentum is quantized**.

with and integers satisfying the condition . The operators that

We derive the functional form of the

Jim Branson 2013-04-22