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Related Concept Videos

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Consider a system comprising several point masses. The coordinates of the center of mass for this system can be expressed as the summation of the product of each mass and its position vector divided by the total mass:
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An electric dipole is a system of two equal but opposite charges, separated by a fixed distance. This system is used to model many real-world systems, including atomic and molecular interactions. One of these systems is the water molecule, but only under certain circumstances. These circumstances are met inside a microwave oven, where electric fields with alternating directions make the water molecules change orientation. This vibration is equivalent to heat at the molecular level.
Consider a...
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In steady, incompressible flow through a long, straight pipe with a uniform cross-section, the flow in the central region (far from the pipe walls) is irrotational. This irrotational nature means that fluid particles do not rotate around their axes, and a scalar function called the velocity potential, represented by ϕ, can be used to describe their movement. In irrotational flows, the velocity field V is defined as the gradient of the velocity potential:
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A neutral atom consists of a positively charged nucleus surrounded by a negatively charged electron cloud. When placed in an external electric field, the external electric force pulls the electrons and nucleus apart, opposite to the intrinsic attraction between the nucleus and the electrons. The opposing forces balance each other with a slight shift between the center of masses of the nucleus and the electron cloud, resulting in a polarized atom. On the other hand, a few molecules, like water,...
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In electrostatics, the electric field can be written as the negative gradient of the potential. In magnetostatics, the zero divergence of the magnetic field ensures that the magnetic field can be expressed as the curl of a vector potential. This potential is known as the magnetic vector potential.
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The simplest case of a surface charge distribution is the uniformly charged disk. Calculating its electric field also helps us calculate the electric field of a large plane of charge.
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Related Experiment Video

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Generation and Coherent Control of Pulsed Quantum Frequency Combs
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Dirac Green function for angular projection potentials.

Rudolf Zeller1

  • 1Institute for Advanced Simulation, Forschungszentrum Jülich and JARA, D-52425 Jülich, Germany.

Journal of Physics. Condensed Matter : an Institute of Physics Journal
|November 3, 2015
PubMed
Summary

This study analytically describes the Dirac Green function

Area of Science:

  • Quantum mechanics
  • Relativistic quantum chemistry

Background:

  • The Dirac Green function is crucial for relativistic quantum chemistry.
  • Calculating it accurately for complex potentials is challenging.

Purpose of the Study:

  • To develop an analytical method for the Dirac Green function.
  • To enable exact relativistic density-functional calculations.

Main Methods:

  • Utilizing projection potentials in angular momentum space.
  • Employing non-local potentials for angular dependence.
  • Handling radial dependence with computational precision.

Main Results:

  • Analytical description of the Dirac Green function's angular dependence.
  • Exact calculation of the Green function is feasible.

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  • Generalization to multi-cell potentials demonstrated.

    • Conclusions:

    • This approach offers a new perspective for relativistic density-functional theory.
    • Enables exact density determination for approximating local potentials.