The pseudo-potential dominates the behavior of the wavefunction at the originif the potential is less singular than
, the equation becomes
The dominant term at the origin will be given by some power of
Higher powers of
are OK, but are not dominant.
Plugging this into the equation we get
There are actually two solutions to this equation,
The first solution,
, is well behaved at the origin (regular solution).
The second solution,
, causes normalization problems at the origin