Test of Density Functional Approximation for an Atom in a Strong Magnetic Field
The density functional formalism for the ground state of a Fermion fluid in a central potential is reviewed. Kohn and Sham’s procedure is replaced by an explicit evaluation of the kinetic energy density functional, which is carried out via a semiclassical approximation to the path integral representation of the appropriate Green’s function. This technique is generalized to an imposed uniform magnetic field, using a short time path integral approximation. The special case of an uncoupled harmonic atom in a magnetic field is solved exactly. Its energy and spatial extent are evaluated at low, medium, and high field strength, and compared with the density functional results. Several suggestions are made as to how the anisotrophy which is lost in the latter approach can be recovered.
KeywordsUniform Magnetic Field Classical Path Path Integral Representation Density Functional Approximation Density Functional Formalism
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