The function Fn,l (r) ;the radial part of of the pseudo-wave function ?k (r, ? , ? ) is expressed in terms of ion-core electron density, ?n,l (r) and its relation with the radial part Pn,l (r ) of Hartree- Fock wave function. A new mathematical function psl (x) called as pseudo-spherical function has been developed which is similar to other mathematical functions, and helpful in determining many types of electron densities. The physical and mathematical developments on various aspects such as functional densities have been described. It is further emphasized that Fn,l (r) and Pn,l (r) functions and core electron density at different electronic states of the atom that both the functions posses strong correlationship. Study concludes that the present development resulted into an innovative simpler path in the orientation of condensed matter as well as Mathematical Physics.
1) The given relationship is a strong evidence which relates the Pseudo spherical concept and Hartree Fock concept. The present pseudo –wave functional description follows fully the frame work of pseudo-potential theory, which gives orientation to the physical problems of Condensed matter Physics.
2) The wave function Fn,l (r) may describe directly the dynamics of pseudo-atom in a simple way as compared to Hartree or Hartree-Fock approaches. Fn,l(r) function is also more suitable and open an easy way for finding core electron density ?n,l (r) of metals.
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