approximation
(noun)
An imprecise solution or result that is adequate for a defined purpose.
Examples of approximation in the following topics:
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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.
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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.
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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.
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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.
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Eddington Approximation
- Because the intensity is close to isotropic we can approximate it by
- The Eddington approximation is the result that
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Dipole Approximation
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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.
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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.
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Rosseland Approximation
- Let's get a better approximation to the radiation field
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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.