  The stationary states of a particle in a central potential are usually taken
as a product of an angular part Phi and a radial part R. The function R
satisfies the so-called radial equation and is usually solved by demanding R to
be finite at the origin. In this work we examine the reason for this
requirement in the case of a two-dimensional (2D) central force problem. In
contrast to some claims commonly accepted, the reason for discarding solutions
with divergent R(0) is not the need to have a normalizable wave function. In
fact some wave functions can be normalized even if R is singular at the origin.
Instead, here we show that if R is singular, the complete wave function psi =
Phi R fails to satisfy the full Schrodinger equation, but follows a equation
similar to Schrodinger's but with an additional term containing the 2D Dirac
delta function or its derivatives. Thus, psi is not a true eigenfunction of the
Hamiltonian. In contrast, there are no additional terms in the equation for
wave functions psi built from solutions R that remain finite at the origin. A
similar situation also occurs for 3D central potentials as has been shown
recently. A comparison between the 2D and 3D cases is carried out.
