3D Problems Separable in Cartesian Coordinates

We will now look at the case of **potentials that separate in Cartesian coordinates**.
These will be of the form.

In this case, we can solve the problem by **separation of variables**.

The left hand side of this equation depends only on , while the right side depends on and . In order for the two sides to be equal everywhere, they

The
part of the solution satisfies the equation

Treating the other components similarly we get

and the total energy is

There are only a few problems which can be worked this way but they are important.