Potential energy Hamiltonian function relationship

We next apply these classical relationships to the rigid diatomic molecule. Since the molecule is rotating freely about its center of mass, the potential energy is zero and the classical-mechanical Hamiltonian function H is just the kinetic energy of the two particles,... 

The crucial simplification in the density functional scheme is the relationship between the interacting system, whose energy and density we seek, and the fictitious, non-interacting system for which we solve Eqs. (9) and (10). This can be studied by considering the interaction A/ r — r and varying X from 0 (non-interacting system) to 1 (physical system). This is done in the presence of an external potential, such that the ground state of the Hamiltonian,... 

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