**Kinetic Energy of Inhomogeneous Electron Gas**

Figure 1: Summary of the electron-electron interactions (excluding coulomb effects) in (a) the Hartree approximation, (b) the Hartree-Fock approximation, (c) the local density approximation and (d) the local spin density approximation which allows for different interactions for like-unlike spins. ^{3}

**Reference**

1. Ronald Bass. Kinetic energy of an electron gas. Phys. Rev. B **32**[4] 2670 (1985)

2. R. Baltin, N.H. March. Electron and kinetic energy densities from Dirac's equation for a model semi-infinite inhomogeneous electron gas. J. Phys. A: Math. Gen. **20** 5517-5528 (1987)

3. http://cmt.dur.ac.uk/sjc/thesis/thesis/node13.html#local

4. Gerrit E. w. Bauer. General operator ground-state expectation values in the Hohenberg-Kohn-Sham density -functional formalism. Phys. Rev. B **27**[10] 5912-5918 (1983)

5. http://en.wikipedia.org/wiki/Kinetic_energy

6. J. Hautman, L. M. Sander. Nonlocal exchange-correlation energy in very inhomogeneous systms: Quasi-two-dimensional electron layers. Phys. Rev. B **30**[12] 700-704 (1984)

7. S. B. Elegba. Thomas-Fermi-Dirac theory of impurity screening in materials in the non-local density approximation. J. Phys. F: Met. Phys. **17** 1357-1363 (1987)

Kinetic energy of electron gas