ABSTRACT
In the application of the extended Thomas-Fermi (ETF) method to a many-fermion system, only those terms in the ft expansion will be included that give finite contribution to the energy. The ETF model yields the smooth part of the level density and other quantities. It will be derived from the E. Wigner-J. G. Kirkwood. It discusses the ETF density variational method and its use for obtaining in a self-consistent way the average parts of the energy and other observables of a many-fermion system in its ground state. Finally, a numerical smoothing of the level density may also be done, by replacing each delta function spike by an appropriate smoothing function, like a Gaussian or a Lorentzian. Since the TF approximation is obtained by replacing the sum over the quantum states by the integral over classical phase space, it is not surprising that it amounts to taking the inverse Laplace transform of the classical canonical partition function.
