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High frequency approximation

 

 
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High frequency approximation
 
 
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A high frequency approximation (or "high energy approximation") for scattering
Scattering

Scattering is a general physical process where some forms of radiation, such as light, sound, or moving particles,are forced to deviate from a straight trajectory by one or more localized non-uniformities in the medium through which they pass....
 or other wave
Wave

A wave is a disturbance that propagates through space and time, usually with transference of energy. While a mechanical wave exists in a medium , waves of electromagnetic radiation can travel through vacuum, that is, without a medium....
 propagation problems, in physics
Physics

Physics is the natural science which examines basic concepts such as energy, force, and spacetime and all that derives from these, such as mass, charge, matter and its Motion ....
 or engineering
Engineering

Engineering is the discipline and profession of applying Technology and science knowledge and utilizing natural laws and physical resources in order to design and implement materials, structures, machines, devices, systems, and process that safely realize a desired objective and meet specified criteria....
, is an approximation whose accuracy increases with the size of features on the scatterer or medium relative to the wavelength of the scattered particles.

Classical mechanics
Classical mechanics

Classical mechanics is used for describing the motion of macroscopic objects, from projectiles to parts of machinery, as well as astronomical objects, such as spacecraft, planets, stars, and galaxies....
 and geometric optics are the most common and extreme high frequency approximation, where the wave or field properties of, respectively, quantum mechanics
Quantum mechanics

Quantum mechanics is a set of principles underlying the most fundamental known description of all physical systems at the microscopic scale . Notable amongst these principles are both a dual wave-like and particle-like behavior of matter and radiation, and prediction of probabilities in situations where classical physics predicts certaintie...
 and electromagnetism
Electromagnetism

Electromagnetism is the physics of the electromagnetic field, a field which exerts a force on Elementary particles with the property of electric charge and which is reciprocally affected by the presence and motion of such particles....
 are neglected entirely.

Less extreme approximations include, the WKB approximation
WKB approximation

In physics, the WKB approximation, also known as WKBJ approximation, is the most familiar example of a semiclassical calculation in quantum mechanics in which the wavefunction is recast as an exponential function, semiclassically expanded, and then either the amplitude or the phase is taken to be slowly changing....
, physical optics
Physical optics

In physics, physical optics, or wave optics, is the branch of optics which studies interference, diffraction, polarization, and other phenomena for which the ray approximation of geometric optics is not valid....
, the geometric theory of diffraction, the uniform theory of diffraction
Uniform theory of diffraction

In numerical analysis, the uniform geometrical theory of diffraction is a high frequency method for solving electromagnetic scattering problems from electrically small discontinuities or discontinuities in more than one dimension at the same point....
, and the physical theory of diffraction.






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A high frequency approximation (or "high energy approximation") for scattering
Scattering

Scattering is a general physical process where some forms of radiation, such as light, sound, or moving particles,are forced to deviate from a straight trajectory by one or more localized non-uniformities in the medium through which they pass....
 or other wave
Wave

A wave is a disturbance that propagates through space and time, usually with transference of energy. While a mechanical wave exists in a medium , waves of electromagnetic radiation can travel through vacuum, that is, without a medium....
 propagation problems, in physics
Physics

Physics is the natural science which examines basic concepts such as energy, force, and spacetime and all that derives from these, such as mass, charge, matter and its Motion ....
 or engineering
Engineering

Engineering is the discipline and profession of applying Technology and science knowledge and utilizing natural laws and physical resources in order to design and implement materials, structures, machines, devices, systems, and process that safely realize a desired objective and meet specified criteria....
, is an approximation whose accuracy increases with the size of features on the scatterer or medium relative to the wavelength of the scattered particles.

Classical mechanics
Classical mechanics

Classical mechanics is used for describing the motion of macroscopic objects, from projectiles to parts of machinery, as well as astronomical objects, such as spacecraft, planets, stars, and galaxies....
 and geometric optics are the most common and extreme high frequency approximation, where the wave or field properties of, respectively, quantum mechanics
Quantum mechanics

Quantum mechanics is a set of principles underlying the most fundamental known description of all physical systems at the microscopic scale . Notable amongst these principles are both a dual wave-like and particle-like behavior of matter and radiation, and prediction of probabilities in situations where classical physics predicts certaintie...
 and electromagnetism
Electromagnetism

Electromagnetism is the physics of the electromagnetic field, a field which exerts a force on Elementary particles with the property of electric charge and which is reciprocally affected by the presence and motion of such particles....
 are neglected entirely.

Less extreme approximations include, the WKB approximation
WKB approximation

In physics, the WKB approximation, also known as WKBJ approximation, is the most familiar example of a semiclassical calculation in quantum mechanics in which the wavefunction is recast as an exponential function, semiclassically expanded, and then either the amplitude or the phase is taken to be slowly changing....
, physical optics
Physical optics

In physics, physical optics, or wave optics, is the branch of optics which studies interference, diffraction, polarization, and other phenomena for which the ray approximation of geometric optics is not valid....
, the geometric theory of diffraction, the uniform theory of diffraction
Uniform theory of diffraction

In numerical analysis, the uniform geometrical theory of diffraction is a high frequency method for solving electromagnetic scattering problems from electrically small discontinuities or discontinuities in more than one dimension at the same point....
, and the physical theory of diffraction. When these are used to approximate quantum mechanics
Quantum mechanics

Quantum mechanics is a set of principles underlying the most fundamental known description of all physical systems at the microscopic scale . Notable amongst these principles are both a dual wave-like and particle-like behavior of matter and radiation, and prediction of probabilities in situations where classical physics predicts certaintie...
, they are called semiclassical
Semiclassical

In physics, the adjective semiclassical has different precise meanings depending on the context. All these meanings usually refer to some approximation, limit or situation that combines quantum mechanics and classical mechanics aspects in a given problem....
 approximations.

See also

  • Electromagnetic modeling