Appearance of anomalies in the Takatsuka-McKoy variational method: An illustrative example

It is demonstrated that the method of the fractional functional proposed by Takatsuka and McKoy, and the variational method of Moe and Saxon and of Kolsrud are identical. In particular, we show that the method is, contrary to Takatsuka and McKoy's claim, not free of anomalies; it implies the incorporation of the boundary conditions, it does not satisfy a minimum principle, and suffers from inconsistency. In order to illustrate the validity of our arguments, we investigate the $s$-wave scattering of electrons by Yukawa potentials.