Fisher information and semiclassical methods

Abstract

Using the Frieden and Soffer principle of extreme physical information we present a method for the construction of WKB wave functions that avoids the matching problem between the classically allowed and forbidden regions. When this formalism is applied in conjunction with the semiclassical methods for N-fermion systems, it provides one with Thomas-Fermi and Wigner-Kirkwood densities, valid beyond the turning points that also include shell effects. The method is illustrated with reference to both the sextic bistable and the Morse potential.