We show that the Lagrangian for interacting nonrelativistic particles can be coupled to external gauge field and metric tensor in a way that exhibits a nonrelativistic version of general coordinate invariance. We explore the consequences of this invariance on the example of the degenerate Fermi gas at infinite scattering length, where conformal invariance also plays an important role. We find t...

We show that a simple and straightforward rational approximation to the Thomas– Fermi equation provides the slope at origin with unprecedented accuracy and that relatively small Padé approximants are far more accurate than more elaborate approaches proposed recently by other authors. We consider both the Thomas–Fermi equation for isolated atoms and for atoms in strong magnetic fields.

By using the scaling method we derive the virial theorem for the relativistic mean field model of nuclei treated in the Thomas–Fermi approach. The Thomas–Fermi solutions statisfy the stability condition against scaling. We apply the formalism to study the excitation energy of the breathing mode in finite nuclei with several relativistic parameter sets of common use. PACS: 21.60.-n; 24.30.Cz; 21...

In this paper, we propose Hermite collocation method for solving Thomas-Fermi equation that is nonlinear ordinary differential equation on semi-infinite interval. This method reduces the solution of this problem to the solution of a system of algebraic equations. We also present the comparison of this work with solution of other methods that shows the present solution is more accurate and faste...

We study normal state properties of an interacting Fermi gas in an isotropic harmonic trap of arbitrary dimensions. We exactly calculate the first-order perturbation terms in the ground state energy and chemical potential, and obtain simple analytic expressions of the total energy and chemical potential. At zero temperature, we find that Thomas-Fermi approximation agrees well with exact results...