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Topic: Wave mechanics

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	Wave equation -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-08)
		Variations of the wave equation are also found in (The branch of quantum physics that accounts for matter at the atomic level; an extension of statistical mechanics based on quantum theory (especially the Pauli exclusion principle)) quantum mechanics and (A generalization of special relativity to include gravity (based on the principle of equivalence)) general relativity.
		The basic wave equation is a (Click link for more info and facts about linear differential equation) linear differential equation which means that the amplitude of two waves interacting is simply the sum of the waves.
		More realistic differential equations for waves allow for the speed of wave propagation to vary with the frequency of the wave, a phenomenon known as (Spreading widely or driving off) dispersion.
	www.absoluteastronomy.com /encyclopedia/w/wa/wave_equation.htm (778 words)

	CE 597F Wave Mechanics (Site not responding. Last check: 2007-10-08)
		Waves are an incredibly important physical phenomenon because they arise in many, many different ways, from fluid to solids to electromagnetics.
		For the example of surface water waves, the equilibrium state is the static, quiescent fluid and the restoring force is gravity.
		This important result reveals that the speed of a wave is, in general, dependent upon the wavelength, and by association the frequency, of the wave.
	www.engr.psu.edu /ce/hydro/hill/teaching/ce597f/ce597f_wavebasics.html (1641 words)

	Wave Mechanics:(4 Wave Theoretical)
		The composite or summational wave is the summation of the four component sinusoidal waves.
		The pattern of the composite wave is the result of the summation and changes of the various underlying waves.
		If two or more waves are moving up or down simultaneously, they cause what is called either positive or negative constructive interference, respectively, meaning that the combined sum of the energies of these two or more waves creates a greater positive or negative amplitude summational wave.
	www.sacredscience.com /baumring/wavemechanics.htm (1836 words)

	WAVE MECHANICS (Site not responding. Last check: 2007-10-08)
		This demonstrates the lack of structural integrity in a water wave; water being a granular medium at the quantum level of atoms and molecules.
		Pick the peak of one good-sized wave and attempt to follow it along at the general speed of the waves.
		Ether Waves are all of the frequencies of electromagnetic waves.
	ca.geocities.com /rayredbourne/docs/38.htm (1758 words)

	Quantum Mechanics 1
		When Born showed that the solution of Schrodinger's wave equation could be interpreted as a non-observable object used only as an intermediary to calculate relative probabilities of the various allowed outcomes of an experiment, and when Bohr and Heisenberg solidified this interpretation (the so-called "Copenhagen interpretation") Schrödinger objected strongly.
		Whatever the correct wave equation might be, it should contain the relations between wave and particle properties that seem to apply for particles (or waves) moving freely through space.
		Solutions of the wave equation in the e-m case are the E and B fields of the wave.
	www.phy.duke.edu /courses/100/lectures/QM1/QM1.html (1249 words)

	Wave Mechanics (Site not responding. Last check: 2007-10-08)
		Waves confined to a certain space are called the standing waves.
		The amplitude of the standing wave (maximum displacement) depends on a position.
		The greater the n, the higher the energy of the standing wave.
	www.chemistry.nmsu.edu /studntres/chem111/resources/notes/wave_mechanics.html (191 words)

	Heisenberg - Quantum Mechanics, 1925-1927: The Uncertainty Principle (Site not responding. Last check: 2007-10-08)
		They gladly welcomed Schrödinger's alternative wave mechanics when it appeared in early 1926, since it entailed more familiar concepts and equations, and it seemed to do away with quantum jumps and discontinuities.
		Most of the young men who created matrix mechanics were ready to move into teaching positions as professors, and the older generation of theoretical physicists was beginning to vacate positions at German universities.
		Heisenberg's family was exerting pressure on the young man to capture one of the vacancies at the same time that his best work, matrix mechanics, seemed to be overshadowed by wave mechanics.
	www.aip.org /history/heisenberg/p08.htm (958 words)

	Wave Mechanics and Quantum Physics
		Quantum mechanics was developed in the early twentieth century in response to several observed phenomena which could not be described by classical physics.
		Quantum mechanics borrows heavily from classical wave mechanics and the first part of the course will be devoted to developing a solid understanding of the theory of classical vibrations and waves.
		The entire volume is devoted to quantum mechanics although much of it requires a knowledge of linear algebra beyond that required for this course.
	www.eg.bucknell.edu /~dcollins/teaching/2004Spring/Phys222 (908 words)

	CACR Wave Calculator (Site not responding. Last check: 2007-10-08)
		The wave height is not allowed to exceed 0.8 of the water depth and is denoted `breaking' if this condition is met.
		Additional results are the wave energy, E, per square meter of the water surface, the wave energy flux per meter of crest length, E_f, and the pressure response factor at the bottom, K_p.
		Note: There is a very good approximation for the wave length given the water depth and wave period that does not require numerical iteration due to Fenton and McKee (1989) as quoted by Fenton, The Sea, vol.
	www.coastal.udel.edu /faculty/rad/wavetheory.html (253 words)

	New Method Predicts Monster Waves
		Wave forecasts made by the United States deal with data grid points that are 15.5 miles apart, which misses the fine points crucial to boaters.
		Waves affect those on land too, moving sediment around in ways that pulls the soil right out from under buildings, endangers bridges and other coastal structures, and changes shipping lanes and harbor shapes overnight.
		This rare photo of a rogue wave was taken by first mate Philippe Lijour aboard the supertanker Esso Languedoc, during a storm off Durban in South Africa in 1980.
	www.livescience.com /forcesofnature/050503_monster_waves.html (1185 words)

	Wave Mechanics; Animated de Broglie phase wave (Site not responding. Last check: 2007-10-08)
		Note that the speed of the phase wave (phase velocity) exceeds that of the particle (group velocity).
		Note that, in accordance with the de Broglie theory, the phase of the phase wave at the position of the particle always exactly matches the instantaneous phase of the internal periodic phenomenon associated with the particle, though (except for massless particles) the particle and the phase wave move, or propagate, with different velocities.
		The constant match between the phase of the phase wave and the phase of the internal periodic phenomenon at the position of the particle is illustrated above by the invariable coincidence of the
	www.davis-inc.com /physics/wavegrph.html (398 words)

	Bohmian Mechanics
		Bohmian mechanics, which is also called the de Broglie-Bohm theory, the pilot-wave model, and the causal interpretation of quantum mechanics, is a version of quantum theory discovered by Louis de Broglie in 1927 and rediscovered by David Bohm in 1952.
		Bohmian mechanics is of course as much a counterexample to the Kochen-Specker argument for the impossibility of hidden variables as it is to the one of von Neumann.
		Bohmian mechanics is manifestly nonlocal: The velocity, as expressed in the guiding equation, of any one of the particles of a many-particle system will typically depend upon the positions of the other, possibly distant, particles whenever the wave function of the system is entangled, i.e., not a product of single-particle wave functions.
	plato.stanford.edu /entries/qm-bohm (10692 words)

	Discrete Wave Mechanics: Multidimensional Systems -- Wall 84 (10): 3091 -- Proceedings of the National Academy of ...
		Discrete wave mechanics is pursued further by extending the one-dimensional treatment to two (or more) dimensions in the light of explicit momentum considerations.
		Cognizance is taken of the effect of particle motion on mass and hence on the interactions between components of motion in different directions.
		Accordingly, the separation of variables is most directly accomplished by factoring the principal energy parameter in conjunction with factoring the wave vector expression itself.
	www.pnas.org /cgi/content/abstract/84/10/3091 (171 words)

	Wave Mechanics
		The wave function of the electron obeys a reasonably simple mathematical equation.
		For example, a free particle is described by a wave packet that is localized in space.
		I believe that this theory of wave mechanics can be used to explain current atomic theory.
	www.msu.edu /~russe153/swavemechanics.htm (125 words)

	Kantian Quantum Mechanics, Metaphysic of Space
		The act of observation, which collapses the wave function, is conformable to the Kantian act of synthesis, by which phenomenal objects are introduced into consciousness and subjected to the categories of the understanding.
		Although chance in quantum mechanics has often been argued as allowing for free will, a free cause is still a very different thing from a random cause, which doesn't need mind or self or intention.
		Since the speed of a traveling wave is measured in the inertial frame of reference of its medium, this implies that the velocity of light occurs relative to the velocity of the ether.
	www.friesian.com /space-2.htm (5616 words)

	Experimental Methods
		This course will study aspects of wave motion arising in many fluidmechanical systems, and students will be introduced to fundamental ideas such as dispersion, group velocity, as well as advanced topics including ray theory, non-linear propagation, shocks, solitary waves.
		On successful completion of the course unit students will understand the physical and mathematical reasons for wave motion and be able to formulate and solve simple problems concerning the propagation ofwaves in dispersive and non-dispersive media.
		Waves in a continuously stratified fluid: Internal gravity waves.
	www.ma.man.ac.uk /DeptWeb/MScCourses/APPMSC/newmtp/wavemec.htm (158 words)

	Broglie's wave hypothesis (from quantum mechanics) -- Encyclopædia Britannica (Site not responding. Last check: 2007-10-08)
		More results on "Broglie's wave hypothesis (from quantum mechanics)" when you join.
		By analogy with the wave and particle behaviour of light that had already been established experimentally, the French physicist Louis de Broglie suggested (1924) that particles might have wave properties in addition...
		Light, for example, appearing in some respects as a continuous electromagnetic wave, on the submicroscopic level is emitted and absorbed in discrete amounts, or quanta; and for light of a given wavelength, the magnitude of all the quanta emitted or absorbed is...
	www.britannica.com /eb/article-77508?tocId=77508 (894 words)

	WAVE MECHANICS ULTRATOOLS: PLUG-IN SUITE FOR PRO TOOLS
		UltraTools is a suite of plug-ins by Wave Mechanics that works with Digidesign's Pro Tools TDM system, as well as third-party programs that utilize the Pro Tools24 MIX hardware.
		SoundBlender Wave Mechanics groups two separate plug-ins called PitchBlender and TimeBlender into a single module dubbed SoundBlender.
		A large number of interesting presets have been programmed by the engineers at Wave Mechanics, but don't be afraid to tweak-the results will never fail to yield surprises.
	mixonline.com /mag/audio_wave_mechanics_ultratools (2122 words)

	Wave Mechanics; Prince Louis de Broglie
		A consequence of de Broglie's reasoning is that a phase wave, often referred to as the "pilot" wave, appears to accompany the particle.
		Yet, modern introductions to quantum mechanics often fail to emphasize that this phase wave arises as an inevitable consequence of de Broglie's assumption of the internal periodic phenomenon of the particle and the transformation laws of the special theory of relativity.
		Given de Broglie's assumptions, quantum mechanics, which is to say the study of the behavior and interpretation of the phase wave, is the study of an inherently relativistic phenomenon.
	www.davis-inc.com /physics (869 words)

	McGraw-Hill AccessScience: Wave mechanics
		By 1915, experiments on the diffraction (bending) of x-rays into special directions by crystals had established that x-rays were electromagnetic waves, akin to visible and infrared light, but of much shorter wavelength than those other electromagnetic radiations.
		Thus, some experiments with electromagnetic radiation seemingly can be understood only by visualizing the radiation as waves, while other experiments on the same radiation seemingly require that the radiation be visualized as a stream of particles.
		This quite unintuitive wave-particle duality manifested by electromagnetic radiation is all the more remarkable in that the particlelike properties associated with the radiation, namely the energy and momentum of its photons, are given in terms of its wavelength, a concept that seemingly has no meaning except in a wave context.
	www.accessscience.com /Encyclopedia/7/74/Est_740400_frameset.html (217 words)

	Chapter 7: Wave Mechanics and Wave Particle Duality
		He worked out the exact solutions of the wave equation for the hydrogen atom, and the results perfectly agreed with the known energy levels of these atoms, seemingly without any of the complications and metaphysical speculations associated with the uncertainty principle.
		Schrödinger believed that the intensity of the wave at a point in space represented the 'amount' of the electron that was present at that point.
		This indicated that the simple interpretation of the wave equation as a description of the physical matter waves in ordinary space, as was originally assumed by Schrödinger himself, is incorrect.
	www.faqs.org /docs/qp/chap07.html (827 words)

	Links to Waves, Water Waves, Solitons, Internal Waves (Site not responding. Last check: 2007-10-08)
		Here is an overview of water waves including a section on beach erosion and ripples.
		A very accessible discussion of the wave nature of matter can be found at the indicated University of Virginia site.
		This is a short article on internal wave solitons and "death waves".
	www.fluidmech.net /msc/f_linkw.htm (566 words)

	WATER WAVE MECHANICS FOR ENGINEERS AND SCIENTISTS (Site not responding. Last check: 2007-10-08)
		The formulation and solution of the governing boundary value problem for small amplitude waves are developed and the kinematic and pressure fields for short and long waves are explored.
		The transformation of waves due to variations in depth and their interactions with structures are derived.
		The application of the water particle motions and pressure fields are applied to the calculation of wave forces on small and large objects.
	www.worldscibooks.com /engineering/1232.html (276 words)

	Experiments on Wave Interference
		Well, we talked about how light travels in waves, and waves can "cancel each other out" if the high point of one meets the low point of another.
		The bottom wave on the left is the sum of the two waves above it.
		Light behaves basically the same way as water waves, but it's harder to visualize because it's happening in three dimensions, and you can't see the light until it hits something.
	www.colorado.edu /physics/2000/schroedinger (404 words)

	Quantum Physics: David Bohm. Bohmian Wave Mechanics, David Bohm Biography
		For Bohm, the insights of quantum mechanics and relativity theory point to a universe that is undivided and in which all parts merge and unite in one totality.
		In Bohmian mechanics a system of particles is described in part by its wave function, evolving, as usual, according to Schrödinger's equation.
		Bohmian mechanics inherits and makes explicit the nonlocality implicit in the notion, common to just about all formulations and interpretations of quantum theory, of a wave function on the configuration space of a many-particle system.
	www.spaceandmotion.com /Physics-David-Bohm-Holographic-Universe.htm (7201 words)

	Exambot - Wave Mechanics Quiz (Site not responding. Last check: 2007-10-08)
		Find the phase difference between the initial two waves.
		A cord is agitated by an oscillator, producing a wave that is described by the equation
		a) Both w and k are positive, so the wave must travel in the positive-x direction.
	www.exambot.com /cgi/exam/show.cgi/physics/waves/2019.ex?a (293 words)

	Grand Unified Theory: Wave Theory - Quantum Mechanics
		two loops are one wave, one QUANTUM, or one whole wave in which each of the loops constitutes only half of the wave formation (this structure is also pervasive in the field of musicology, see picture to the right).
		The most prominent argument that has been raised against the two camps is that while the rules of quantum mechanics work for subatomic particles, they do not apply to larger formations.
		Wave theory has indeed contributed one basic formation that bridges the ideas of both camps and holds true for all that exists in our universe — everything.
	www.grandunifiedtheory.org.il /quantum.htm (460 words)

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