  The angular wave functions for a hydrogen atom are well known to be spherical
harmonics, and are obtained as the solutions of a partial differential
equation. However, the differential operator is given by the Casimir operator
of the $SU(2)$ algebra and its eigenvalue $l(l+1) \hbar^2$, where $l$ is
non-negative integer, is easily obtained by an algebraic method. Therefore the
shape of the wave function may also be obtained by extending the algebraic
method. In this paper, we describe the method and show that wave functions with
different quantum numbers are connected by a rotational group in the cases of
$l=0$, 1 and 2.
