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Topic: Wave function

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	Wavefunction - Wikipedia, the free encyclopedia
		In this representation, ket vectors are represented by functions on the continuous index set and the inner product of the Hilbert space corresponds to the integral of the product of two wavefunctions.
		If the energy spectrum of a system is (partly) discrete, such as for a particle in an infinite potential well or the bound states of the hydrogen atom, then the position representation is continuous while the momentum representation is partly discrete.
		Wave mechanics are most often used when the number of particles is relatively small and knowledge of spatial configuration or 'shape' is important.
	en.wikipedia.org /wiki/Wave_function (728 words)

	Wave Function of the Universe(s)
		is a wave function that describes all the possible various possible states of a particle.
		The wave function is assumed to be quite large near our own universe, so there is a good chance that our universe is the correct one, as we expect.
		Since the wave function is supposedly vanishingly small for these other universes, we do not expect that our universe will make a quantum leap to them in the near future.
	www.geocities.com /capecanaveral/hangar/6929/h_kaku2.html (903 words)

	Neuroscience-Net Article 1996-011 (Site not responding. Last check: 2007-11-07)
		In this commentary, possible neural mechanisms of wave function collapse and their relation to human conscious experience are considered, as well as their potential involvement in neuropathologies that may be quantum mechanical in nature.
		Thus quantum mechanics incorporates an operation, collapse of the wave function (also called reduction of the state vector where the state vector is the linear sum of the complexly weighted possible alternative states) which is inherently probabilistic, rather than deterministic in the classical Newtonian sense.
		Thus, this interpretation is compatible with the hypothesis of Stapp (1993) and simultaneously similar to the hypothesis of "orchestrated objective reduction" of the wave function (Penrose, 1994; Hameroff and Penrose, 1996)[Footnote 3].
	www.neuroscience.com /manuscripts-1996/1996-011-miller/1996-011-miller.html (9612 words)

	The wave function
		These groups of sine waves representing all phenomena, such as a particle, an atom, planet, galaxy, objects, a thought, word, concepts or ideas, mind, etc. may be immensely complex, comprising waves in fractal groups extending into higher dimensions, in which their phase relationship is of key importance.
		One of the main reasons why the wave function in current quantum physics has to be considered fictional is because it is expressed by the resultant of many sub-wave functions representing probabilities or attributes of entities of the natural world in the form of respective orthogonals.
		The wave function is not linear or of a single level but multidimensional and can be envisaged as groups of sine waves within groups displaced along the gradient 3D to 4D, governed by frequency.
	www.users.globalnet.co.uk /%7Enoelh/Wavefunction.htm (2197 words)

	Mailgate: sci.physics.cond-matter: Re: Wavefunction for three particles (Site not responding. Last check: 2007-11-07)
		I think that whether or not we can think of the wave function as somehow physical (as opposed to an expression of our knowledge), it is clear that it is impossible to view the wave function of several particles as a matter wave.
		That's because such a wave function is a function on configuration space, rather than physical space.
		In contrast, a two-particle wave function has the form Psi(x1, y1, z1, x2, y2, z2), which gives information about the probability of finding the first particle at position (x1,y1,z1) and the second particle at position (x2,y2,z2).
	mailgate.supereva.it /sci/sci.physics.cond-matter/msg01191.html (333 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.
		Nevertheless, the wave function is an amplitude with phase, its average square has a physical meaning (probability density) and is subject to interference and diffraction.
	www.du.edu /~jcalvert/waves/wavefun.htm (5715 words)

	Stream Function Wave Theory (Site not responding. Last check: 2007-11-07)
		By varying the wave height (rerunning the applet by using the Reset button and editing the wave parameters), you can show the effects of wave amplitude on wave length (and on wave speed, since the speed of the wave is the wave length divided by the wave period.
		The order of the Stream function wave is a measure of how nonlinear the wave is. In deep water, the order can be low, 3 to 5 say, while, in very shallow water, the order can be as great as 30.
		This is an attempt by the Stream Function theory to develop a periodic wave train, not a new wave discovery (Dalrymple and Solano, J. Waterway, Port, Coastal and Ocean Eng, 1986).
	www.coastal.udel.edu /faculty/rad/streamless.html (433 words)

	why wave function real
		That the wave function of n particle is a function of 3n variables doesn’t mean, that we are confronted with an obscure 3n dimensional space, but it means only that the particles are related to each other and that they behave collectively as a whole or that they are entangled.
		The use of complex valued wave function indicates only that the wave function is made of two entities: A magnitude and a phase.
		Thus we think there is no evidence why we should accept the existence of a pointlike entity beside the wave function and why we should stop to try to solve problems 1, 4 and 5 from purely wave mechanical point of view.
	physics-qa.com /html/kqm13.htm (889 words)

	The Ontological Interpretation of the Wave Function of the Universe
		The Ontological Interpretation of the Wave Function of the Universe
		An interpretation of the wave function of the universe that assumes a background Everett-type theory results in a novel "quantum mechanical world/world of experience" split that differs from the.'split" that pertains to interpretations of ordinary quantum mechanics.
		Given this denial that his remarks are to be read as suggesting an ontological interpretation of the wave function of the universe, we may allow that Isham cannot properly be charged with a contradiction or lack of specificity in an ontological interpretation of the equation.
	www.qsmithwmu.com /the_ontological_interpretation_of_the_wave_function_of_the_universe.htm (9089 words)

	Wave function (Site not responding. Last check: 2007-11-07)
		An approximate wave function for the boson ground state that we use for a trial function is
		There is a deficiency with the trial wave function that leads to undersampling when three particles are in close proximity.
		One solution is to use a guiding function, which differs from the trial wave function, for the diffusion and branching.
	archive.ncsa.uiuc.edu /Science/CMP/dewing/thesis/node43.html (428 words)

	Brain wave Functions Alpha Beta Theta Brainwaves
		It is well known that the brain is an electrochemical organ; researchers have speculated that a fully functioning brain can generate as much as 10 watts of electrical power.
		These beta waves are of relatively low amplitude, and are the fastest of the four different brainwaves.
		Beta waves are characteristics of a strongly engaged mind.
	brain.web-us.com /brainwavesfunction.htm (1028 words)

	The Wave Equation and Permutation of Rays
		Thus the wave equation simply expresses the requirement that the sum of the values of the wave function just before and just after a given event equals the sum of the values on either side of the event.
		It also suggests that the "topology of implication" of the wave function is not Euclidean, but is more accurately represented by the indefinite "metric" of Voigt and Lorentz, with singular measures along the diagonals.
		In full 3+1 dimensional spacetime the spherically symmetrical wave equation can be reduced to the same form as the 1+1 dimensional equation, except that the space wave function is normalized by r, and the parameter x is replaced with the radius r, so each "light ray" actually represents a sequence of expanding and converging shells.
	www.mathpages.com /home/kmath251/kmath251.htm (1305 words)

	Series Solutions of the Wave Equation
		The second column is essentially the rate of change of the wave function at the initial instant as a function of radial position.
		The form of the recursive relation implies that we can fully specify the entire wave function (for the case p = q = 0) simply by specifying the value at the origin for all time.
		is an even function of time, i.e., symmetrical with respect to time about any instant in which the wave function is stationary.
	www.mathpages.com /home/kmath247/kmath247.htm (1160 words)

	Stephen Hawking's Cosmology and Theism
		Hawking's atheistic dreadnought is a 'wave function of the universe'.
		If the wave function is 'the amplitude for the Universe to appear [supernaturally uncaused] from nothing' and the modulus of the amplitude squared gives the probability, then the probability contra Hartle and Hawking is zero if it is true that the universe cannot begin to exist supernaturally uncaused.
		Hawking's wave function law enables the probabilistic history of the universe to be calculated once the initial state of the universe is known.
	www.infidels.org /library/modern/quentin_smith/hawking.html (3089 words)

	Quantum Physics: The Nodal Theory: Chapter 11: Nodal Wave Function
		This wave is independent of the observer or his velocity, as it must be if it represents the objective NWF of the particle.
		The size of the wave packet also is subjective, and in a different way; it is dependent not just on the observer's state of motion, but on the extent of his knowledge of the particle's past history.
		The wave of one particle does not interfere with that of another, but there are circumstances in which the NWF corresponding to one segment of a particle's history can become superposed on that from another segment to produce interference effects.
	www.c-parr.freeserve.co.uk /quantum/ch11.htm (4455 words)

	Wave-function collapse (Site not responding. Last check: 2007-11-07)
		It is customary to ascribe a wave-function to the state of the experiment before an actual measurement is made, and then to speak of the wave-function collapsing to one of the eigenstates of the wave-equation just at the moment of registration.
		But what if one views things somewhat differently: suppose the wave equation describes NOT a physical state, not something that changes during the course of the experiment, in particular at the point of registration (observation), but rather as a description of the symmetries of the experiment as whole, undivided, setup and registration.
		The measurement phase and the setup phase are not separately described by the wave function and equation.
	www.panix.com /~dave/quantum/recent/collapse.html (510 words)

	The Microanthropic Principle
		We have a wave function and a differential equation—the Schroedinger equation—to predict the evolution of the wave function with absolute certainty.
		It's only the square of the magnitude of the wave function that yields the probabilities of classical outcomes (the value of the wave function is a complex number which has magnitude and phase).
		In the many-universe theory, the square of the magnitude of the wave function is interpreted as the "density" of universes, but as long as the "rare" universes exist on the same footing as the "dense" ones, we can't really talk about their probabilities.
	www.relisoft.com /Science/Physics/MicroAnt3.html (1184 words)

	Bohmian Mechanics
		For the evolution of the wave function, Bohmian mechanics is formulated in terms of Schrödinger's equation alone.
		And as Bell has shown, using the connection between the wave function and the predictions of quantum theory concerning experimental results, this nonlocality cannot easily be argued away (see Section 2).
		This nonlocal effect upon the conditional wave function of particle 2 follows from combining the standard analysis of the evolution of the wave function in the EPR-Bohm experiment with the definition of the conditional wave function.
	plato.stanford.edu /entries/qm-bohm (10692 words)

	Untitled Document (Site not responding. Last check: 2007-11-07)
		Choosing the Shape of the Wave Function: Depending upon the total energy and potential energy in the chosen Region, decide whether the wave functions will be oscillating or decreasing.
		After choosing the type of wave function (Oscillating or Decreasing) change the parameters of the wave function using the appropriate tab.
		In case of Oscillating wave function, change the "Amplitude", "Wavelength", and "Phase" of the wave function using the sliders in each of the tabs.
	phys.educ.ksu.edu /vqm/html/wfsketcher.html (541 words)

	User Macro Document - texture_wave
		The macro allows the frequency, phase and amplitude of the wave function to be controlled.
		This automatically increments the phase of the wave function hence moving the pulse-wave through the alpha channel of the image.
		Integer parameter that specifies which type of wave function should be used to generate the output.
	www.iavsc.org /repository/express/pages/twave/twave.shtml (931 words)

	Many-body wave function and fermion node - research L. Mitas (Site not responding. Last check: 2007-11-07)
		For some configurations of electrons the wave function is zero because of fermion antisymmetry.
		The shades of blue color represent values of negative part of the wave function while the positive part (see a movie) is located in the complementary (empty) space.
		Note that the wave function fulfills the periodical boundary conditions as the infinite solid is represented by the periodically repeating supercell.
	altair.physics.ncsu.edu /fnode.html (296 words)

	ZPEnergy.com - The Electron Wave Function - Our next Energy Revolution
		Known as the electron wave function, the wave function consists of a series of standing waves, and these waves constitute a form of energy that we could conceivably now tap using cutting edge technology.
		Opto-electronic signal waves are amplified by wells because the wave functions interact with the electrons in the conduction bands of direct gap semiconductors with a transfer of energy to the wave function and an amplification of this wave.
		We know from observation that the work function of quantum dots for example is smallest between 2 and 5 nanometers, and goes up again as the size of the dot is reduced further.
	www.zpenergy.com /modules.php?name=News&file=article&sid=720 (1175 words)

	Wave Function Optimization (Site not responding. Last check: 2007-11-07)
		The general problem of function optimization is a well-studied area.
		The main difficultly in applying these techniques to optimizing VMC wave functions is noise - we only get stochastic estimates for function values or gradients.
		This is possible with a Newton method, where the first and second derivatives of the function are computed, and the number of iterations needed for convergence hopefully is small.
	archive.ncsa.uiuc.edu /Science/CMP/dewing/thesis/node27.html (237 words)

	Quantum Scattering Experiments (Site not responding. Last check: 2007-11-07)
		The wave funcition Psi(x,t) is initially a guassian wave packet moving to the right.
		The wave function, Psi(x,t), is shown in the shaded region below.
		The boundary conditions are periodic, so that waves which exit to the right will return on the left.
	www.physics.brocku.ca /faculty/sternin/teaching/mirrors/qm/packet/wave-map.html (131 words)

	DUBSI help: 1-cos wave (Site not responding. Last check: 2007-11-07)
		The total duration of the wave and the starting time both have to be equal to or greater than zero.
		The amplitude may be positive, yielding a 'hill-shaped' wave function, or negative, yielding a 'valley-shaped' wave.
		The sign of the amplitude will be reflected in the shape of the block-icon.
	home.wanadoo.nl /dutchroll/dubsi/wavefcn.html (78 words)

	The Orbitron: a gallery of atomic orbitals and molecular orbitals
		See below for links to images of the wave functions of the other 4f wave functions.
		Schematic plot of the 4f wave function ψ
		The line graph on the left is a plot of values along along the x = y = z line.
	www.shef.ac.uk /chemistry/orbitron/AOs/4f/wave-fn.html (157 words)

	Time [Internet Encyclopedia of Philosophy]
		Imagine what the initial conditions at the edge of a pond must be like to produce correlated, incoming, concentric water waves that would expel the rock and leave the water surface smooth.] Some philosophers argue that temporal asymmetry, but not temporal priority, can be analyzed in terms of causation.
		The standard answer is that we are measuring the advancing phase of the quantum wave function, an esoteric kind of change.
		It expresses a propositional function; that is, it is used to express different propositions on different occasions.
	www.iep.utm.edu /t/time.htm (15789 words)

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