http://vixra.org/pdf/0908.0079v1.pdf
see equation (2.21) the reasoning to get this (2.21) goes from page 9 to page 14
should be the inverse of the potential denoted by $ x(V) $ proportional to the half-derivative ?
i mean something $$ x(V)= C\frac{d^{1/2}}{dV^{1/2}}N(V) $$
instead of the author's claim $$ X(V)= A\frac{dN(V)}{dV} $$
here A and C are constants