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Topic: Wave vector

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	Wave vector - Wikipedia, the free encyclopedia
		The wave vector has magnitude indicating wavenumber (reciprocal of wavelength), and the direction of the vector indicates the direction of wave propagation.
		The wave vector is most useful for generalizing the equation of a single wave into a description of a family of waves.
		As long as the family of waves all travel in the same direction and with the same wavelength, a single wave vector is valid for the entire family.
	en.wikipedia.org /wiki/Wave_vector (481 words)

	Plane wave - Wikipedia, the free encyclopedia
		In the physics of wave propagation (especially electromagnetic waves), a plane wave (also spelled planewave) is a constant-frequency wave whose wavefronts (surfaces of constant phase) are infinite parallel planes of constant amplitude normal to the phase velocity vector.
		where i is the imaginary unit, k is the wave vector, ω is the angular frequency, and a is the (complex) amplitude.
		for electromagnetic waves in an isotropic medium), whereas a longitudinal wave is one in which the amplitude vector is parallel to k (e.g.
	en.wikipedia.org /wiki/Plane_wave (463 words)

	essay 2
		This fundamental wave structure is defined as the vector wave because it establishes a specific color charge position based on octaves of the same color charge.
		Given points 66-67, the harmonic development of the vector wave is limited to the bonding of 3 consecutive vector waves which is defined as a vector set.
		The first is the complete alpha wave, the second is partial alpha wave consisting of 1 charged spin sub-particle and 1 completely neutral reverse spin sub-particle, the third consists of 1 charged spin sub-particle, 1 neutral spin sub-particle, and 1 completely neutral reverse spin sub-particle, the fourth consists of 2 completely neutral sub-particles.
	www.spectrummuse.com /essay_2.htm (2896 words)

	PlanetMath: Schrödinger's wave equation
		The Schrödinger wave equation is considered the most basic equation of non-relativistic quantum mechanics.
		This is in fact a little imprecise since the wave function is, in a way, a statistical tool: it describes a large number of identical and identically prepared systems.
		This is version 15 of Schrödinger's wave equation, born on 2005-02-16, modified 2005-07-21.
	planetmath.org /encyclopedia/WaveFunction.html (364 words)

	segment_4
		Vector 0P is the variable or moving vector and, like the moving pencil point, its head traces the path of the straight line that we are interested in.
		The process for generating the vector parametric equations for the reverse wave segment is the same as for the forward segment, but with a vector that has the opposite sense (opposite flow) of the forward wave vector.
		Vector 0Q, like vector 0P, is the moving variable vector (tail is fixed, but head moves and traces the line of interest) which will trace the path of our reverse wave line segment.
	www.levity.com /eschaton/sheliak/seg_4.html (875 words)

	Strangeway: Wave Dispersion, Ray Propagation, and AKR - Section 5 (Site not responding. Last check: 2007-09-17)
		Additionally, while a wave may be propagating perpendicularly to the magnetic field, the wave vector can be parallel to the edge of the auroral arc.
		Since the wave polarization for the unstable mode is generally similar to the R-X mode, it might be argued that the wave will propagate away from the arc in the Z mode.
		Since there is no freedom in choosing the wave vector direction with respect to the gradient along the field, unlike perpendicular propagation as discussed above, we may be more confident in our estimate of reflection coefficients at the low-altitude cutoff for the unstable mode.
	www-ssc.igpp.ucla.edu /~strange/AKR_85/akr85_5.html (2095 words)

	Advanced diffraction
		If we shift the head of the B vector to the tail of the A vector, it doesn't change its x component, even as it rotates, so the x component of the sum of the two vectors defines the sum of the two waves.
		The result is a cosine wave with the same wavelength but a different amplitude and phase that are given simply by the sum of two vectors.
		The incoming X-ray is considered as a plane wave, with peaks in the electric field occurring on planes perpendicular to the wave vector, separated by the wavelength.
	www-structmed.cimr.cam.ac.uk /Course/Adv_diff1/Diffraction.html (4324 words)

	Electromagnetic waves
		Not all EM waves are sinusoidal plane waves, but all electromagnetic waves can be viewed as a linear superposition of sinusoidal plane waves traveling in arbitrary directions.
		E is the electric field vector and B is the magnetic field vector of the EM wave.
		(a) The wave is reflected by the mirror.
	electron9.phys.utk.edu /optics421/modules/m1/emwaves.htm (1063 words)

	Acousto
		Acousto-optic devices are based on the periodic modulation of the optical index of refraction caused by an acoustic wave propagating in a transparent material.
		Assume an acoustic wave is traveling in a transparent material with a wave vector pointing into the x-direction.
		The coupling between the between the acoustic wave and the electromagnetic wave is a result of the modulation of the optical index of refraction caused by an acoustic wave.
	electron9.phys.utk.edu /optics507/modules/m7/acousto.htm (1026 words)

	Wave Functions
		In fact, most physical waves, such as those of sound in air or waves on the surface of water, or an electromagnetic wave moving along a transmission line, or light propagating down a fibre, are not precisely described by an equation of this type.
		Waves on the surface of deep water are also strongly dispersive, the phase velocity being proportional to the square root of the wavelength.
		For electromagnetic waves in which only one polarization state exists, or the two states are mixed equally, as in white light, and for phenomena that are nearly independent of polarization, such as diffraction, scalar waves give an adequate description.
	www.du.edu /~jcalvert/waves/wavefun.htm (5715 words)

	The Tom Bearden Website
		We also understand that a zero-gradient of a scalar is a zero vector, so that the scalar itself may be taken to be a zero vector.
		Since the waves are 180 degrees out of phase, the exterior resultant wave has a zero electric field and a zero magnetic field.
		Therefore it is a "zero-vector" wave, or "scalar" wave.
	www.cheniere.org /books/part4/s22.htm (530 words)

	The Optics Project - Modules - Reflection/Refraction - Theory
		be the wave vector of the reflected wave.
		be the wave vector of the transmitted wave.
		is a unit vector in the direction of the propagation vector of the transmitted wave.
	webtop.msstate.edu /top/mod_refl_the.html (320 words)

	Radialwave, LLC - Science (Site not responding. Last check: 2007-09-17)
		Poynting vector describes the the flow of energy (Power) through a surface in terms of electric and magnetic properties.
		The rate of energy transport per unit area is described by the Poynting vector, (S=1/mu(0))* E x B. The Poynting vector describes the magnitude of energy per unit of time that propagates and what direction it propagates.
		The quarter-wave transmitting antenna may be efficiently loaded up to about twice its resonant wave length by the insertion of antenna inductance, or it may be shortened down to about three-fourths of its resonant wave length by the use of a series capacitance.
	www.radialwave.com /science.htm (1106 words)

	Electromagnetic Waves
		Briefly stated, the incoming wave causes dipoles to vibrate at the surface of the dielectric, which creates a wave travelling at speed c that interferes with the original wave and extinguishes it in the medium, and also a new wave travelling at speed c/n that propagates in the dielectric as described above.
		The angle of incidence is the angle between the normal to the interface and wave vector of the incident wave.
		The wave vector of the transmitted, or refracted, wave also lies in the plane of incidence, and the ratio of the sine of the angle of incidence to sine of the angle of refraction is the same as the ratio of the propagation velocities.
	www.du.edu /~jcalvert/phys/emwaves.htm (9513 words)

	segment_3
		The Simple Bi-directional Wave, as described thus far, is fundamentally a collection of [x, y] integer data points, that are generated by the FOD number set and the performance of several subsequent mathematical operations.
		The forward and reverse waves are properly superimposed with the correct endpoint closure, and the data set integers are connected with straight-line segments.
		These vector definitions will be used to formulate the vector parametric equations of the generalized line segment, the basis for the Simple Bi-directional Wave and the wave expansions that follow.
	www.levity.com /eschaton/sheliak/seg_3.html (1293 words)

	Vector Optical Heterodyning
		Vectorial optical signal of CLBS is considered in the framework of Fraunhofer diffraction of two plane vector waves (with polarization described as Jones vectors) by a single particle in case of periodical modulation of Jones vector one of them.
		It is known that vector wave is the common state of monochromatic electromagnetic radiation.
		Vector features of optical waves for problem of sizeandvelocity control by using method of optical vector heterodyning has several evidence advantages with regard to traditional using of scalar wave beating.
	www.gpi.ru /~sukhodol/iecec/3/index.html (2861 words)

	Energy band formation
		A wave that travels neither to the left nor to the right is a standing wave: it does not go anywhere.
		There are two different standing waves that can occur: one representing the difference of a right and a left-directed wave and one representing the sum of a right and a left-directed wave.
		The standing wave 2 piles up electrons around the positive ion cores, which means that the average potential energy will be lower than for a free traveling wave (constant probability density).
	www.mtmi.vu.lt /pfk/funkc_dariniai/quant_mech/bands.htm (1339 words)

	Quantum Gravity:The Properties of Mass and Space-time Curvature as Wave Dispersion, by Todd Desiato
		It is a function of the wave velocity and decreases as the particle accelerates in the direction of steepest decent along the velocity gradient.
		For instance, the alignment of the spin vector of a positive energy particle along the z-axis is the direction of the magnetic field vector, where the spin axis vector points from South to North in the magnetic field.
		The wave velocity as seen by a free particle is a function of the dielectric susceptibility of the environment as shown by equation (24), which in turn is a function of the polarizability of the particles it contains.
	www2.3dresearch.com /~alistolmar/Dispersion.html (3281 words)

	NEUTRON ONLINE HELP
		Given the space group and the phonon symmetry specified by the wave vector q, the program examines the inelastic neutron scattering activity of the corresponding phonons for all possible types of scattering vectors Q=H-q, where H is a reciprocal lattice vector.
		Using the distribution of the reciprocal lattice vectors (Brillouin zones) into types with respect to the symmetry group of the scattering vector, it is possible to show that Brillouin zones belonging to the same type are characterized by the same set of selection rules.
		As the wave vector we are considering is GM, its little group coincides with the space group Pnma and the 8 little group irreps for both cases are simply related to the irreps of the point group mmm.
	www.cryst.ehu.es /rep/neutron/neutron_help.html (1272 words)

	Two Waves of Differing Wavelength (Site not responding. Last check: 2007-09-17)
		In the third example of figure 2.6, the frequency of the wave depends only on the direction of the wave vector, independent of its magnitude.
		An example of the superposition of two waves with different directions and wavelengths is shown in figure 2.10.
		The wave fronts are perpendicular the the vector average of the two wave vectors,
	hep.physics.uoc.gr /~konstant/p102/raymond/node24.html (479 words)

	Spherical wave expansion of a vector plane wave
		In discussing the scattering or absorption of electromagnetic radiation by localized systems, it is useful to be able to express a plane electromagnetic wave as a superposition of spherical waves.
		Consider, first of all, the expansion of a scalar plane wave as a set of scalar spherical waves.
		is the wave vector with the spherical coordinates
	farside.ph.utexas.edu /teaching/jk1/lectures/node102.html (276 words)

	Plane Waves (Site not responding. Last check: 2007-09-17)
		The wave fronts are constant phase surfaces separated by one wavelength.
		The wave vector is normal to the wave fronts and its length is the wavenumber.
		The large arrow is a vector called the wave vector, which defines (1) the direction of wave propagation by its orientation perpendicular to the wave fronts, and (2) the wavenumber by its length.
	hep.physics.uoc.gr /~konstant/p102/raymond/node21.html (537 words)

	String Wave Equation
		The four equations (B.1) through (B.5) can be combined into a single vector wave equation that expresses the propagation of waves on the string having three displacement components.
		Furthermore, the three displacement components of the wave are coupled together at all points along the string, so that the wave equation is no longer separable into three independent 1D wave equations.
		This is the linearized wave equation for the string, based only on the assumptions of elasticity of the string, and strain magnitudes much less than unity.
	ccrma-www.stanford.edu /~jos/dwtheory/String_Wave_Equation.html (522 words)

	Astron. Astrophys. 331, L21-L24 (1998) (Site not responding. Last check: 2007-09-17)
		The nonlinear coupling of Langmuir waves, electromagnetic waves and ion-acoustic waves is governed by the generalized Zakharov equations (Akimoto 1988, Rizzato and Chian 1992, Chian and Abalde 1997)
		of the transverse electromagnetic wave is orthogonal to the wave vector
		For a given Langmuir pump wave energy level, the growth rate of the convective instability is higher than the growth rate of the absolute instabilities.
	aa.springer.de /papers/8331002/2300l21/sc1.htm (1305 words)

	HOLOGRAPHIC PROJECTION TO AN ARBITRARY PLANE FROM SPHERICAL NEAR-FIELD MEASUREMENTS
		This calculation is straightforward and fairly simple since we automatically have the plane wave spectrum as a function of the x-y components of the propagation vector.
		The equations that are used for the interpolation from angular coordinates to plane wave vector coordinates are
		Mathematical expressions for the unit vectors are obtained from Equation (5) and the equations that define the vector components for the different coordinate systems.
	www.nearfield.com /amta/AMTA01_AN_02.htm (2016 words)

	NR_article
		For a non-uniform film the calculation of critical wave vector is more complicated, but it is roughly a function of the average SLD of the film.
		is the reflectance of the wave from the surface.
		, the complex amplitude of the reflected wave, is called the reflectivity, and it is this quantity that is measured.
	www.ncnr.nist.gov /programs/reflect/NR_article/NR_article.html (1673 words)

	Motion in Two and Three Dimensions
		In that case Snell's law tells us how the direction of the wave vector changes, while the dispersion relation combined with the constancy of the frequency gives us information about the change in the magnitude of the wave vector.
		For matter waves a similar procedure works, though the details are different, because we seek the consequences of a change in potential energy rather than a change in the index of refraction.
		The vector character of this expression yields an additional possibility over the one dimensional case, where the work is either positive or negative depending on the direction of
	www.physics.nmt.edu /~raymond/classes/ph13xbook/node89.html (627 words)

	Math Tutorial - Four-Vectors
		Also shown in figure 5.1 is a spacetime vector or four-vector which represents the frequency and wavenumber of the wave, which we refer to as the wave four-vector.
		In three dimensions we define a vector as a quantity with magnitude and direction.
		Thus, for instance, the wavenumber for some wave may be zero in the primed frame, which means that the wavenumber and frequency in the unprimed frame are related to the frequency in the primed frame by
	www.physics.nmt.edu /~raymond/classes/ph13xbook/node50.html (435 words)

	Diffraction - Wikimedia Commons
		Diffraction vector: difference between the wave vector of the scattered wave and the incident wave
		When the diffraction vector K stays on the same direction, this means that wave vectors of the the incidence and scattered waves move symetrically
		The intersection of the sphere of the nodes of the reciprocal lattice and the Ewald sphere show that the wave vector of the diffused wave whene there is diffraction form a cone
	commons.wikimedia.org /wiki/Diffraction (207 words)

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