Dirac single particle energy

A numerical analysis of the energy values (Hess 1986 Molzberger and Schwarz 1996) and also perturbation theory (Kutzelnigg 1997) shows that the eigenvalues of the DKH Hamiltonian for a single particle agree with the results of the Dirac equation to order c 4. Note that this is the same order in which deviations in the... 

The Furry bound state interaction picture of quantum electrodynamics76 relies on an expansion of the second-quantized electron field operator in terms of single-particle solutions of the Dirac equation for a static external field. This external field may be thought of as some mean atomic or molecular potential, whose single-particle spectrum can be divided into positive- and negative-energy branches. This can always be done for the usual elements of the Periodic Table, although problems arise for super-heavy atomic nuclei. 

In this work a simple analytical atomic density model is obtained from the expression of a modified Thomas-Fermi-Dirac model with quantum corrections near the nucleus as the minimization of a semiexplicit density functional. The use of a simple exponential analytical form for the density outside the near-nucleus region and the resolution of a single-particle Schrodinger equation with an effective potential near the origin allows us to solve easily the problem and obtain an asymptotic expression for the energy of an atom or ion in terms of the nuclear charge Z and the number of electrons N. 

Fermi-Dirac statistics applies to particles with a half-integral spin, such as electrons, protons and neutrons. Such particles are called fermions. No two identical fermions can occupy a single (quantised) energy level. As spin can differentiate between two otherwise identical fermions, two fermions, with opposed spins, can occupy each energy level. Fermi-Dirac statistics specify the the probability. Pi, that an energy level, E,-, will be occupied is given by ... 

The surprising implication is that Dirac s equation does not allow of a self-consistent single-particle interpretation, although it has been used to calculate approximate relativistic corrections to the Schrodinger energy spectrum of hydrogen. The obvious reason is that a 4D point particle is without duration and hence undefined. An alternative description of elementary units of matter becomes unavoidable. Prompted by such observation, Dirac [3] re-examined the classical point model of the electron only to find that it has three-dimensional size, with an interior that allows superluminal signals. It all points at a wave structure with phase velocity > c. 

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