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Related Concept Videos

Potential Due to a Polarized Object01:29

Potential Due to a Polarized Object

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,...
Polar Coordinates: Problem Solving01:27

Polar Coordinates: Problem Solving

Directional radiation patterns are central to antenna analysis, as they illustrate how signal strength varies with direction. These patterns are often modeled using polar plots, where the radial distance from the origin represents signal intensity at a given angle. A commonly used idealized form is the four-lobed rose curve, which captures the concept of directional beams in a simplified mathematical form.The four-lobed rose curve, described by r = cos⁡(2θ), features four symmetric lobes, each...
Measuring Reaction Rates03:09

Measuring Reaction Rates

Polarimetry finds application in chemical kinetics to measure the concentration and reaction kinetics of optically active substances during a chemical reaction. Optically active substances have the capability of rotating the plane of polarization of linearly polarized light passing through them—a feature called optical rotation. Optical activity is attributed to the molecular structure of substances. Normal monochromatic light is unpolarized and possesses oscillations of the electrical field in...
Group Polarization01:01

Group Polarization

Group polarization is the strengthening of an original group attitude following the discussion of views within a group (Teger & Pruitt, 1967). That is, if a group initially favors a viewpoint, after discussion the group consensus is likely a stronger endorsement of the viewpoint. Conversely, if the group was initially opposed to a viewpoint, group discussion would likely lead to stronger opposition.
Graphs of Polar Equations01:17

Graphs of Polar Equations

The polar coordinate system represents points using a distance from a central point (the pole) and an angle from a reference direction (the polar axis). Unlike rectangular coordinates, polar coordinates are ideal for graphing curves with radial symmetry or periodic behavior.Some general forms of graphs in polar coordinates include the following:Equation of a Circle (Centered at the Pole):A graph where the radius remains constant for all angles traces a circle centered at the pole:Equation of a...
Polar Curves01:19

Polar Curves

The spirograph is a versatile tool for visualizing the relationship between geometry and mathematical representation. In particular, it demonstrates how polar coordinates offer an alternative framework for describing curves in comparison to Cartesian coordinates. Instead of specifying a point by its horizontal and vertical displacements (x, y), polar coordinates use a radius r, the distance from the origin, and an angle θ, measured counterclockwise from the polar axis. This system is...

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Related Experiment Video

Updated: Jul 18, 2026

Polarization-Sensitive Two-Photon Microscopy for a Label-Free Amyloid Structural Characterization
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Published on: September 8, 2023

Polarization propagator for x-ray spectra.

Ulf Ekström1, Patrick Norman, Vincenzo Carravetta

  • 1Department of Physics, Chemistry and Biology, Linköping University, SE-581 83 Linköping, Sweden.

Physical Review Letters
|December 13, 2006
PubMed
Summary

This study introduces a new method for calculating X-ray spectra using density functional theory. It accurately predicts X-ray absorption cross sections without needing to compute excited states.

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Area of Science:

  • Computational Chemistry
  • Quantum Chemistry
  • Spectroscopy

Background:

  • Calculating X-ray spectra is crucial for material analysis.
  • Traditional methods often require explicit computation of excited states, which is computationally intensive.

Purpose of the Study:

  • To develop a direct method for calculating X-ray absorption cross sections.
  • To implement a polarization propagator approach within density functional theory.

Main Methods:

  • Formulation of a resonant-convergent first-order polarization propagator approach.
  • Implementation within density functional theory (DFT).

Main Results:

  • Direct calculation of X-ray absorption cross sections at specific frequencies.
  • Elimination of the need to explicitly address excited states.
  • Spectrum quality depends solely on the chosen density functional.

Conclusions:

  • The developed polarization propagator method offers an efficient way to predict X-ray spectra.
  • This approach simplifies calculations by bypassing the need for excited state computations.
  • The accuracy is directly linked to the underlying density functional theory approximations.