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Topic: Wavefunction

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	Wavefunction - Wikipedia, the free encyclopedia
		The spatial wavefunction associated with a particle in one dimension is a complex function
		In this context the wavefunction associated with a particular state may be seen as an expansion of the state in a basis for the vector space H.
		An example of this is the spacial wavefunction associated with a particle in one dimension which expands the state of the particle in terms of states with definite position.
	en.wikipedia.org /wiki/Wavefunction (1227 words)

	Wavefunction collapse - Wikipedia, the free encyclopedia
		In certain interpretations of quantum mechanics, wavefunction collapse is one of two processes by which quantum systems apparently evolve according to the laws of quantum mechanics.
		However, when the wavefunction collapses, which is the other process, from an observer's perspective the state seems to "jump" to one of the basis states and uniquely acquire the value of the property being measured that is associated with that particular basis state.
		The cluster of phenomena described by the expression wavefunction collapse is a fundamental problem in the interpretation of quantum mechanics known as the measurement problem.
	en.wikipedia.org /wiki/Wavefunction_collapse (493 words)

	Experimental Model for Collapse of the QuantumWavefunction
		Collapse of the quantum wavefunction is a universal process that involves conscious determination of global mind/brain (mental) states from among a superposition of virtual or potential states.
		The notion that collapse of the wavefunction involves collapse of macroscopic, global mental states rather than microscopic events coordinated by quantum coherence in the brain was pioneered by Henry Stapp (1991; 1993; 1994) in quantum physics and Mark Germine in mind science (1989; 1991; 1993; 1994; 1996).
		Collapse of the wavefunction is the mechanism of consciousness, and actualizes a single state from among a myriad of implicit or unconscious possible states (virtual states).
	www.goertzel.org /dynapsyc/1998/collapse.html (3453 words)

	Wavefunction - Psychology Central (Site not responding. Last check: 2007-10-21)
		The complex square of the wavefunction, $\psi^2\,$ , is interpreted as the probability density associated with the particle's position, and hence the probability that a measurement of the particle's position yields a value in the interval $[a, b]$ is
		The three dimensional case is analogous to the one dimensional case; the wavefunction is a complex function $\psi(x, y, z)\,$ defined over three dimensional space, and its complex square is interpreted as a three dimensional probability density function.
		In this context the wavefunction associated with a particular state may be seen as an expansion of the state in a basis for the vector space $H$ .
	psychcentral.com /psypsych/Wavefunction (1580 words)

	Quantum mechanics postulates
		The wavefunction is assumed here to be a single-valued function of position and time, since that is sufficient to gaurantee an unambiguous value of probability of finding the particle at a particular position and time.
		The wavefunction may be a complex function, since it is its product with its complex conjugate which specifies the real physical probability of finding the particle in a particular state.
		In order to use the wavefunction calculated from the Schrodinger equation to determine the value of any physical observable, it must be normalized so that the probability integrated over all space is equal to one.
	hyperphysics.phy-astr.gsu.edu /hbase/quantum/qm.html (500 words)

	Radial Distribution Functions
		The wavefunctions for the l = 1 levels, the p orbitals, are not spherically symmetric.
		The electronic wavefunction, as we have seen above, describes the distribution of the electron positions in terms of the distance of the electron from the nucleus, r, and the orientaion of the electron relative to the nucleus.
		We can separate the wavefunction into an orientationally dependent part, known as the angular wavefunction, and an orientationally independent part, which is known as the radial wavefunction.
	www.everyscience.com /Chemistry/Inorganic/Atomic_Structure/c.1101.php (576 words)

	Many Worlds Theory FAQ
		In terms of the wavefunction, a world is a decohered branch of the universal wavefunction, which represents a single macrostate.
		In the path-integral picture the wavefunction of a single particle at (x',t') is built up of contributions of all possible paths from (x,t), where each path's contribution is weighted by a (phase) factor of exp(iAction[path]/hbar) wavefunction at (x,t), summed, in turn, over all values of x.
		The wavefunction of a collection of particles/fields exists in a Fock space, where the number of dimensions varies from component to component, corresponding to the indeterminacy in the particle number.
	kuoi.asui.uidaho.edu /~kamikaze/doc/many-worlds-faq.html (15875 words)

	The double slit experiment and the collapse of the wavefunction (Site not responding. Last check: 2007-10-21)
		At any time, the square magnitude of the wavefunction plotted in the figure would be proportional to the probability of detecting the particle at that point, if the whole plane was covered with electron detectors which would be activated at that instant in time.
		The wavefunction itself develops in time according to the time dependent Schroedinger equation under the influence of the potentials, which in this case consists of a barrier region with two slits.
		The shooting up of the wavefunction when it hits the barrier at the center is due to the sharpness of the potential.
	www.fen.bilkent.edu.tr /~yalabik/applets/collapse.html (628 words)

	Chap. 11 Examples
		These methods may be applied to any wavefunction, but the examples shown below utilize one particular wavefunction, namely the wavefunction that describes the ground state of the one-dimensional simple harmonic oscillator system.
		The quantum mechanical wavefunction for the ground state (lowest energy) of this system may be found by solving the Schrodinger equation.
		This is not surprising since the wavefunction for the simple harmonic oscillator is actually obtained by solving the eigenvalue equation for the Hamiltonian operator, i.e.
	classweb.gmu.edu /sdavis/chem332/ex11/ex11.htm (2172 words)

	Wavefunction Collapse (Site not responding. Last check: 2007-10-21)
		During a measurement, the wavefunction instantaneously changes into a state consistent with one of the possible measurement outcomes.
		Some think there is something special about the human mind that is able to collapse wavefunctions, and that the world is a blur of waves until a human observes it.
		The wavefunction of two entangled particles cannot be represented as two waves in a three dimensional space, but as a single wave in a six dimensional space.
	members.aol.com /jmtsgibbs/Collapse.htm (293 words)

	Wavefunction Separability and Size Consistency of the Energy (Site not responding. Last check: 2007-10-21)
		The two different forms of the excitation operator in CI and CC theory have significant consequences for both the energy and wavefunction as the number of electrons is increased or as the (molecular) system is separated into fragments.
		This difficulty also applies to coupled cluster or perturbation-based wavefunctions that use the RHF determinant as a reference; these methods cannot be size consistent for a given molecular system unless the reference wavefunction is size consistent.
		A more general property of the coupled cluster energy which is related to size consistency is ``size extensivity.'' This is a strictly mathematical characteristic of the wavefunction which relates to scaling of the computed energy with respect to the number of correlated electrons and the resulting energy dependence of the wavefunction amplitude equations.
	zopyros.ccqc.uga.edu /lec_top/cc/html/node5.html (862 words)

	Wavefunction Engineering
		Wavefunction engineering refers to the unprecedented ability to specify the localization of carrier wavefunctions in quantum semiconductor heterostructures through control over the growth, geometry, and material composition.
		By changing the geometry or the composition of such a structure it would be possible to alter the wavefunction substantially.
		The aim of the software tools being developed at QSA is to provide precisely the type of freedom, in designing and modeling such structures, that would lead to exploring new mechanisms in electronic transitions and in electronic localization.
	users.rcn.com /qsa/waveeng.html (2757 words)

	Many Worlds Quantum Reality Solution: The Reluctant Messenger - Bible Codes Science Religion Spirituality God Allah ...
		Initially the wavefunction of the system of electrons and two experimenters is: psi>_1 = me,electrons,you> = me>(left,right> - right,left>)you> /sqrt(2) = me,left,right,you> /sqrt(2) - me,right,left,you> /sqrt(2) Neither you or I are yet unambiguously split.
		The wavefunction, in bracket or Dirac notation, is written as symbol>, where "symbol" labels the object.
		It is empirically observed, first noted by Max Born and afterwards called the Born interpretation, that their magnitudes squared represent the probability that, upon observation, that the value of the parameter, labelled by i, will be observed if the system is the state represented by psi>.
	reluctant-messenger.com /many_worlds.htm (16153 words)

	Wavefunction at opensource encyclopedia (Site not responding. Last check: 2007-10-21)
		Due to the commutation relationship of the position and momentum operators, the r-space and k-space wavefunctions are Fourier transform pairs.
		If the energy spectum of a system is discrete, such as for the particle in an infinitely deep box or the bound states of the hydrogen atom, there can actually be both continuous and discrete bases for the same system, and thus either wave mechanics or matrix mechanics may be used to study the system.
		Because of the concrete relationship between the wavefunction and location of a particle in configuration space, many treatments of quantum mechanics at the high-school or early undergraduate level are very wave mechanical.
	www.wiki.tatet.com /Wavefunction.html (554 words)

	2. Some Basic Ideas about Quantum Mechanics
		This is known as the collapse of the wavefunction and the probability of the wavefunction collapsing into a particular eigenfunction depends on how much that eigenfunction contributed to the original superposition.
		When the measurement is made the wavefunction collapses into one of these eigenfunctions, with a probability determined by the composition of the original superposition.
		However, one of the most important characteristics of a wavefunction is that the square of its magnitude is a measure of the probability of finding a particle described by the wavefunction at a given point in space.
	newton.ex.ac.uk /research/qsystems/people/jenkins/mbody/mbody2.html (2015 words)

	Quantum Mechanics: Psi: Physics
		When the wavefunction is a sum of different momentum basis states, the coefficient squared of each of those basis states gives the probability of measuring the particle's momentum to have that value.
		If the wavefunction is in a basis state of energy, then the energy is determined; if it isn't, you can rewrite it as a sum of different basis states of energy, and use their coefficients to find the probabilities of different energy values.
		This change that occurs in the wavefunction as a result of measurement is called the "collapse of the wavefunction," and it forms one of the principal differences between quantum and classical physics.
	www.ncsu.edu /felder-public/kenny/papers/psi.html (11440 words)

	Quantum Psychodynamics of Dreams
		The wavefunction of possible states of the brain is a component of the wavefunction of the universe.
		The wavefunction of the brain, the unconscious mind, is, however, in no way separate from the wavefunction of the universe.
		Separating the brain/universe into two separate entities, the brain and the universe, is a convenience for the sake of discussion. In quantum physics, the state of the universe is described as a single ray in a higher dimensional space or hyperspace.
	www.goertzel.org /dynapsyc/1998/QuantumDreams.html (8082 words)

	Chapter 7
		Consciousness manifests the immanent from the transcendent by collapsing the wavefunction.
		The transcendental realm is hypothesized to contain the wavefunction, yet the wavefunction as normally conceived is a function of time and space, which are absent in the transcendental realm and in fact do not appear "until" wavefunction collapse.
		Thus, the concepts of wavefunctions and wavefunction collapse in the transcendental realm are meaningless.
	faculty.virginia.edu /consciousness/new_page_11.htm (4937 words)

	The Particle in a Box
		a wavefunction for which the integral of its absolute square over all of space is equal to 1 (which signifies that the probability to find the particle somewhere in the integration region is equal to 1).
		Symmetry of the wavefunction: Inspection of our wavefunctions proves that they are either symmetric or antisymmetric against reflection through a mirror plane put at the center of the box.
		The wavefunctions of the threedimensional particle in a box is more difficult to visualize since we lack the forth dimension to plot its amplitude.
	itl.chem.ufl.edu /4412_aa/partinbox.html (1359 words)

	Citebase - Operator ordering and consistency of the wavefunction of the Universe
		The requirement of regularity of the wavefunction has the particular consequence that the probability amplitude, which has been used previously in the literature in discussions of issues such as the prediction of inflation, is likewise ill-defined for certain choices of operator ordering with Vilenkin's boundary condition.
		In particular, it is argued that inflation cannot be confidently regarded as a "prediction" of the tunneling wavefunction, for reasons similar to those previously invoked in the case of the no-boundary wavefunction.
		[27] A. Vilenkin, "Interpretation of the wavefunction of the universe", Phys.
	citebase.eprints.org /cgi-bin/citations?id=oai:arXiv.org:gr-qc/9807075 (1726 words)

	Physics Inside-Out: A Physics of Peace, by Loren Booda
		A virtual wavefunction generates action eigenvalue solutions (in units of h) reciprocal and symmetric to those of its conventional counterpart.
		Wavefunction action eigennumber inversion may provide gravitational, electric or magnetic "singularities" continuity, since it can transform a real, discrete displacement into a virtual, smooth one.
		Wavefunction collapse might occur, say, at such a singularity unique to a spacetime neighborhood, perhaps corresponding to the intersection of geodesics.
	www.quantumdream.net (8185 words)

	Valence-Bond Theory
		We see that the VB wavefunction likes to have one electron near A and one electron near B, whereas the MO wavefunction allows the possibility for 2 electrons on A. The VB wavefunction will therefore describe the dissociation of H
		We say that the VB wavefunction has covalent structures and the MO wavefunction has covelent and ionic structures.
		However, because the MO wavefunction is a determinant, it is possible to add and subtract rows (ie orbitals) to construct functions which are localised.
	www-theor.ch.cam.ac.uk /people/nch/lectures/T0new/node7.html (336 words)

	The Trial Wavefunction
		For bosons the many-body wavefunction is a symmetric function of the positions of the particles.
		The u(r) function is chosen to minimise the energy of the state by increasing the probability of He atoms being separated by a distance where their interaction energy is a minimum.
		Therefore, a Jastrow function is again included in the wavefunction to introduce the effects of correlation between electrons.
	www.tcm.phy.cam.ac.uk /~ajw29/report/node5.html (436 words)

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