# equation for the potential in terms of the phase shift for a rotational invariant potential

let be a potential in 3d invariant under rotations so $V(r)$

in the WKB approximation the phase shifts are given by

$$\delta _{l} (k)= \int_{a}^{\infty}dr \sqrt{k^{2}-2mV(r)-l(l+1)r^{-2}}-\int_{b}^{\infty}dr \sqrt{k^{2}-l(l+1)r^{-2}}$$

here 'a' and 'b' are the zeros of the integrands

my question is from this formula and for fixed l could we obtain the value of the potential $V(r)$ if we know for every l (fixed) the values of the shifts ?? $\delta_{l} (k)$