approximation

Examples of approximation in the following topics:

• The Born-Oppenheimer Approximation

  • The key simplification is that the electrons whip around a lot faster than the nuclei, so one can approximate the situation by assuming that the electrons sit in a particular eigenstate of the potential with the two ions fixed.
  • This in the Born-Oppenheimer approximation.
  • Because the typical energies of the various transitions are well separated we can to a good approximate consider each of them separately, justifying the Born-Oppenheimer approximation.

• Round-off Error

  • A round-off error is the difference between the calculated approximation of a number and its exact mathematical value.
  • A round-off error, also called a rounding error, is the difference between the calculated approximation of a number and its exact mathematical value.
  • Numerical analysis specifically tries to estimate this error when using approximation equations, algorithms, or both, especially when using finitely many digits to represent real numbers.

• Uniform Electric Field

  • Uniformity in an electric field can be approximated by placing two conducting plates parallel to one another and creating a potential difference between them.
  • In such a case there will be slight variations in the field near its edges, but it will be approximately constant throughout every other area.

• Hooke's Law

  • Hooke's law of elasticity is an approximation that states that the extension of a spring is directly proportional to the load applied to it.
  • In mechanics (physics), Hooke's law is an approximation of the response of elastic (i.e., springlike) bodies.
  • Materials for which Hooke's law is a useful approximation are known as linear-elastic or "Hookean" materials.

• Eddington Approximation

  • Because the intensity is close to isotropic we can approximate it by
  • The Eddington approximation is the result that

• Dipole Approximation

• Nuclear Weapons

  • ., "atomic") bomb test released the same amount of energy as approximately 20,000 tons of trinitrotoluene (TNT).
  • The first fusion (i.e., thermonuclear "hydrogen") bomb test released the same amount of energy as approximately 10,000,000 tons of TNT.
  • The death toll from the two bombings was estimated at approximately 200,000 people—mostly civilians, and mainly from acute injuries sustained from the explosions.

• Alpha Decay

  • Alpha decay is by far the most common form of cluster decay, in which the parent atom ejects a defined daughter collection of nucleons, leaving another defined product behind (in nuclear fission, a number of different pairs of daughters of approximately equal size are formed).
  • Alpha particles have a typical kinetic energy of 5 MeV (approximately 0.13 percent of their total energy, i.e., 110 TJ/kg) and a speed of 15,000 km/s.
  • Most of the helium produced on Earth (approximately 99 percent of it) is the result of the alpha decay of underground deposits of minerals containing uranium or thorium.

• Rosseland Approximation

  • Let's get a better approximation to the radiation field

• Spherical and Plane Waves

  • However, many waves are approximately plane waves in a localized region of space.
  • For example, a localized source such as an antenna produces a field that is approximately a plane wave far from the antenna in its far-field region.