Using an exact form for the particle density for N particles moving independently in a linear harmonic oscillator potential, a differential equation is derived for the particle density. This is then shown to be exactly that which is obtained from a local density assumption for the kinetic energy density t, in the form -1/2~lj!; (8 2/8 x ;.. The form of the kinetic energy density functional is then discussed in this example. The implications for wider classes of potential are briefly referred to.
Nuclear cusp conditions are obtained for the full electron-electron interaction energy density as well as for the exchange and correlation energy densities of density-functional theory. Their form is the same as the form of the well known Kato cusp condition for the electron-number density. All these cusp conditions are valid for both the ground and excited states of a molecule or solid.
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