The solution to Schrödinger’s equation in three dimensions is quite complicated in general. Fortunately, nature lends us a hand, since most physical systems are “rotationally invariant”, i.e., depends on the size of , but not its direction! In that case it helps to introduce spherical coordinates, as denoted in Fig. 11.1 .
The coordinates , and are related to the standard ones by
where , and . In these new coordinates we have
(11.7) |