Simple wavefunctions for Yukawa- and Hulthen-type potentials

Based on the general properties of the Yukawa and Hulthen potentials, that they have Coulombic behaviour for small r and are exponentially damped for large r, we have deduced the threshold and asymptotic properties of their e nergy eigenfunctions, We have then developed simple wavefunctions incorpora ting these properties for the lowest and the first excited states for all I values, which give quite accurate energies for a wide range of the screeni ng parameters and which give a clear, physical insight into their structure . The quality of these wavefunctions is analysed in terms of a virial relat ion, a threshold relation and a local energy test.