Continuity of Logarithmic derivative in Scattering theory

I have a problem in understanding why we consider the continuity of the Logarithmic derivative of the wave function at the boundary of the Scattering Potential? I understand that physical arguments require the wavefunction to be continuous, but why the logarithmic derivative?

$$\lim_{r \to a}\frac{r}{\phi} \frac{d}{dr} \phi,$$ where $$a$$ is the length scale of the scattering potential.

• Continuity of the logarithmic derivative guarantees continuity of both the wave function and the derivative of the wave function, which is required in all cases of non-singular scattering potentials (delta-function potentials introduce discontinuities into the derivative of the wave function, but they're pretty unphysical). Mar 4 '16 at 0:25

For a set of wave functions $$f_1$$ and $$f_2$$, boundary conditions are $$f_1=f_2\,$$ and $$f_1' = f_2'$$. Combining these (division makes both equations equal to one) we get $$f_1/f_1' = f_2/f_2$$', which is the logarithmic derivative.