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Related Concept Videos

Electrostatic Boundary Conditions01:16

Electrostatic Boundary Conditions

Consider an external electric field propagating through a homogeneous medium. When the electric field crosses the surface boundary of the medium, it undergoes a discontinuity. The electric field can be resolved into normal and tangential components. The amount by which the field changes at any boundary is given by the difference between the field components above and below the surface boundary.
The surface integral of an electric field is given by Gauss's law in integral form and is related to...
Calculations of Electric Potential I01:15

Calculations of Electric Potential I

Consider a ring of radius R with a uniform charge density λ. What will the electric potential be at point M, which is located on the axis of the ring at a distance x from the center of the ring?
The ring is divided into infinitesimal small arcs such that point M is equidistant from all the arcs. Here, the cylindrical coordinate system is used to calculate the electric potential at point M. A general element of the arc between angles θ and θ + dθ is of the length Rdθ and has a charge of λRdθ.
Electrostatic Boundary Conditions in Dielectrics01:27

Electrostatic Boundary Conditions in Dielectrics

When an electric field passes from one homogeneous medium to another, crossing the boundary between the two mediums imparts a discontinuity in the electric field. This results in electrostatic boundary conditions that depend on the type of mediums the field propagates through.
Consider a case where both the mediums across a boundary are two different dielectric materials. Recall that the electric field and electric displacement are proportional and related through the material's permittivity.
Gauss's Law: Problem-Solving01:10

Gauss's Law: Problem-Solving

Gauss's law helps determine electric fields even though the law is not directly about electric fields but electric flux. In situations with certain symmetries (spherical, cylindrical, or planar) in the charge distribution, the electric field can be deduced based on the knowledge of the electric flux. In these systems, we can find a Gaussian surface S over which the electric field has a constant magnitude. Furthermore, suppose the electric field is parallel (or antiparallel) to the area vector...
Electric Field of a Non Uniformly Charged Sphere01:22

Electric Field of a Non Uniformly Charged Sphere

Gauss's law states that the electric flux through any closed surface equals the net charge enclosed within the surface. This law is beneficial for determining the expressions for the electric field for a particular charge distribution if the electric flux is known.
Consider a non-uniformly charged sphere, for which the density of charge depends only on the distance from a point in space and not on the direction. Such a sphere has a spherically symmetrical charge distribution. Here, the electric...
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,...

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Related Experiment Video

Updated: Jun 29, 2026

Scattering And Absorption of Light in Planetary Regoliths
11:34

Scattering And Absorption of Light in Planetary Regoliths

Published on: July 1, 2019

Elastic scattering using an artificial confining potential.

J Mitroy1, J Y Zhang, K Varga

  • 1ARC Center for Anti-Matter Studies, Faculty of Technology, Charles Darwin University, Darwin NT 0909, Australia.

Physical Review Letters
|October 15, 2008
PubMed
Summary
This summary is machine-generated.

This study introduces a novel method to calculate scattering phase shifts using discrete energies from a confined system. This approach simplifies phase shift determination for complex quantum systems like electron-helium interactions.

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Area of Science:

  • Quantum mechanics
  • Atomic physics
  • Computational physics

Background:

  • Calculating scattering phase shifts is crucial for understanding atomic and molecular interactions.
  • Traditional methods can be computationally intensive, especially for complex systems.
  • An alternative approach using confined systems offers potential computational advantages.

Purpose of the Study:

  • To develop and verify a new method for determining scattering phase shifts.
  • To apply this method to the electron-helium (e(-)-He) system.
  • To investigate the low-energy phase shifts of the e(-)-He system.

Main Methods:

  • Utilizing discrete energies of a scattering Hamiltonian under an artificial confining potential.
  • Exploiting the principle that identical energies in confined Hamiltonians yield identical phase shifts upon potential removal.
  • Employing the stochastic variational method (SVM) for energy calculations.
  • Applying the method to the confined e(-)-He(2S) system.

Main Results:

  • The method was successfully verified on a model problem.
  • Discrete energies for the confined e(-)-He(2S) system were accurately determined using SVM.
  • Low-energy phase shifts for the e(-)-He system were successfully derived from these energies.

Conclusions:

  • The confinement potential method is a viable and efficient approach for calculating scattering phase shifts.
  • This method provides an alternative to traditional scattering calculations.
  • The study successfully determined low-energy phase shifts for the e(-)-He system, contributing to the understanding of electron-atom interactions.