By Lomonaco S.J.

The new program of the rules of quantum mechanics to cryptography has ended in a notable new size in mystery verbal exchange. due to those new advancements, it really is now attainable to build cryptographic communique platforms which realize unau- unauthorized eavesdropping may still it happen, and which offer a warrantly of no eavesdropping should still it now not take place.

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Then, since we know that an elee- Ά Self-Consistent Fields in Atoms tron described by φί has a probability density $ (assuming φί is real : otherwise \φί\2 must be used), we can say immediately that the elec tron density ρ(ι·) in the atom is given by ßto= Σ Φ? Ji) But it is extremely plausible to argue that the potential energy in which the electrons move is that due first to the nucleus, and given by —Ze2\ri for the /th electron at distance ri from the nucleus, and then a contri bution from the electronic charge density given by eqn.

Ji) But it is extremely plausible to argue that the potential energy in which the electrons move is that due first to the nucleus, and given by —Ze2\ri for the /th electron at distance ri from the nucleus, and then a contri bution from the electronic charge density given by eqn. 51). This contribution Ve (r) say, is clearly obtained by solving the Poisson equa tion of electrostatics V2Ve(r)=4neq(r). 52) But from the Schrödinger equation, for an assumed total potential energy V(r), we can find the wave functions ,·, and hence we can cal culate g(r) from eqn.

6) for the self-consistent Thomas-Fermi theory by direct manipulation is possible, the rather lengthy derivation being due, essentially, to Milne (1927). We show below that ---^(è)>+K)'^ Γ / N\2 1 1 1 e* = 0-4841^(0)+(l--)-]z3-. 19) and we obtain the Thomas-Fermi result for atomic binding energies E(Z, Z) = -0-7687Z* —. 20) This result was first obtained by Milne. 7) is stressed. Obviously the coefficient of Z 3 in eqn. 20) is a consequence of the self-consistent Thomas-Fermi theory. Energies of atoms and ions 47 We wish to stress also that examination of Fig.