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Topic: Probability amplitude

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	Amplitude - Wikipedia, the free encyclopedia
		Amplitude is a nonnegative scalar measure of a wave's magnitude of oscillation, that is, magnitude of the maximum disturbance in the medium during one wave cycle.
		The amplitude of sound waves and audio signals conventionally refers to the amplitude of the air pressure in the wave, but sometimes the amplitude of the displacement (movements of the air or the diaphragm of a speaker) is described.
		The square of the amplitude is proportional to the intensity of the wave.
	en.wikipedia.org /wiki/Amplitude (367 words)

	Probability amplitude - Wikipedia, the free encyclopedia
		In quantum mechanics, a probability amplitude is a complex-valued function that describes an uncertain or unknown quantity.
		Probability amplitudes which are not square integrable are usually interpreted as the limit of a series of functions which are square integrable.
		For instance the probability amplitude corresponding to a plane wave corresponds to the 'non physical' limit of a monochromatic source of particles.
	en.wikipedia.org /wiki/Probability_amplitude (404 words)

	QED (inglese)
		Amplitude of probability for the absorption or the emission of a Photon
		j = amplitude probability for the absorption or the emission of a photon
		The greater is the diagram complexity the smaller is the amplitude of probability.
	www.geocities.com /CapeCanaveral/Launchpad/7045/qedteoriai.html (1182 words)

	Quantum Cosmology's Implication of Atheism
		One reason Craig does not understand the H-H probability amplitude is that he confuses the probability amplitude for a 3-space, such as the initial 3-space of our spacetime, with the probability amplitude for an entire 4 dimensional spacetime.
		This probability is, of course, conditional upon the mathematical boundary conditions that belong to the wave function, but it is a fallacy of equivocation to infer from this that the probability is conditional upon concrete things or events (or upon physical boundary conditions).
		Craig (1997:292) asserts that the H-H probability is conditional upon this hypersphere, and that this hypersphere is taken by Hartle and Hawking as an unexplained given.
	www.infidels.org /library/modern/quentin_smith/quantum.html (3570 words)

	Theory: Quantum Mechanics
		A state is described by a quantity that is called a wave-function or probability amplitude.
		The rule for probability in quantum mechanics is that probability is the square of the absolute value of the relevant probability amplitude.
		Furthermore, we cannot even say there is a probability of each process and then add the probabilities, since A+B is not the same number as A For example, let consider A= 5 and B = -3.
	www2.slac.stanford.edu /vvc/theory/quantum.html (1038 words)

	Explanation
		The overall probability amplitude for the transition is the sum not of probabilities but of the probability amplitudes of each of the constituent transitions considered serarately.
		denote the probability amplitude for the transition input i, output j.
		If a machine starts in a particular initial configuration (input) then the probability that after its evolution via a sequence of intermediate configurations it ends up in a specific final configuration (output) is the squared modulus of the sum of all the probability amplitudes of the computational paths that connect the input with the output.
	www.cc.gatech.edu /grads/n/nipun/Projects/quantum/root/node27.html (248 words)

	Why Steven Hawking
		In the case at hand, the probability is for the existence of the three-dimensional spatial slice S (the "three-geometry S" in Hartle and Hawking's parlance), from which the probability of the other states of the universe can be calculated.
		The probability of the existence of the 3-space S is not conditional upon the existence of any concrete object (body or mind) or concrete event (state of a body or mind) or even upon the existence of any quantum vacuum, empty space or time; the probability follows only from the mathematical properties of possible universes.
		But the Hartle-Hawking probability is not dependent on any supernatural states or acts; Hartle and Hawking do not sum over anything supernatural in their path integral derivation of the probability amplitude.
	www.geocities.com /islampencereleri3/why_steven_hawking.htm (7756 words)

	QED Lens (Site not responding. Last check: 2007-10-18)
		So the probability amplitude (which is the length of the arrow, remember) of the photon along any path is equal.
		The length of this new arrow is also a probability amplitude, but this time it tells us how likely it is that the photon will end up at the destination point given the source point.
		The higher the probability amplitude, the higher the probability (though the relationship is quadratic, not linear).
	jhunix.hcf.jhu.edu /~blee27/software/qedlens (1083 words)

	Transformations of a qubit
		The probability amplitude for the whole process is obtained by adding probability amplitudes for all the trajectories followed by the particle.
		These concepts of probability amplitudes and the rules for their manipulations do not fall out of the blue sky, and they are not some axiomatic inventions either.
		In this framework the notion of probability corresponds to the notion of field intensity in classical theory of interference, which is the square of an amplitude.
	beige.ucs.indiana.edu /M743-talk-2/node4.html (1259 words)

	Sense and Nonsense in Quantum Mechanics
		In particular, since the absolute square of the wave displacement represents the probability of finding the particle, once the particle has definitely been found passing through one or the other of the slits, the wave function collapses into a very small wave packet located at the observed position of the particle.
		These laws say that the probability of an event is the sum of the probabilities of alternate independent ways for that event to occur.
		The probability is obtained by adding the alternate probability amplitudes together and taking the absolute square of the sum.
	www.physics.nmt.edu /~raymond/classes/ph13xbook/node71.html (682 words)

	[No title]
		The square of the modulus of the amplitude is
		Thus, the probabilities that are implied by classical theism are inconsistent with the probabilities implied by the Hartle-Hawking wave function of the universe.
		This probability statement is not consistent with the classical theist position that there is 0 percent probability that a Hartle-Hawking universe exist uncaused or with Markosian's scenario where the 99 percent probability obtains only because it is derived from supernatural considerations.
	www.faithfreedom.org /Articles/smith/Hawkings_cosmology.htm (7776 words)

	StarDrive --Feynman Page--Path Integrals
		The Feynman amplitude for the first alternative is the complex number (A1,B2) which has the nucleus from A go to 1, and the nucleus from B goes to 2.
		Wavelike interference of localized particles correspond to cross-modulations where the path of the advanced amplitude is different from the path of the retarded amplitude.
		The total amplitude to start at the point source S and end up at the detection point D is the sum of all of these amplitudes.
	www.stardrive.org /hibbpath.html (3483 words)

	[No title]
		Instead each quantum bit (qubit) has an associated probability amplitude which corresponds to a superposition of basis states 0 and 1.
		We cannot explicitly measure this probability amplitude, in fact measurement of a qubit results in a collapse of the quantum state to one of the basis states.
		The probability of measuring a 0 or 1 however, is determined by the associated probability amplitude.
	pages.cpsc.ucalgary.ca /~curry/webpages/courses/cpsc502.html (599 words)

	American Scientist Online - The Square Root of NOT (Site not responding. Last check: 2007-10-18)
		The amplitude associated with a state determines the probability that the qubit will be found in that state; specifically, the probability is equal to the square of the absolute value of the corresponding amplitude.
		Thus all the entries in the probability matrix are 1/2, and the quantum-mechanical QCF gate appears on first examination to be identical to the classical CF gate.
		Suppose the initial state, at the root of the tree, is a 1, and the first CF gate happens to produce a 0; the probability of this event is 1/2.
	www.americanscientist.org /template/AssetDetail/assetid/24592/page/4 (1069 words)

	Hydrogen Atom Probability Density Applet (Site not responding. Last check: 2007-10-18)
		The reason the Applet graphs the amplitude of Psi instead of the modulus squared (the actual probability of finding the electron an x number of Bohr radii from the nucleus) is due to limitations in the color scale.
		The probability values are significantly smaller than those of amplitude, so when the values are scaled to a number between 0-255 to correspond to an integer value on the red, green, and blue color scale, it doesn't work.
		The probability values are too small and too close together so there isn't much variation in the colors assigned to those points, at least not enough for the naked eye to discern since it operates on a logarithmic scale.
	www.phy.davidson.edu /StuHome/cabell_f/Density.html (397 words)

	Probability and amplitude of novelty responses as a function of the change in contrast of the reafferent image in G. ...
		a novelty response is evoked, and (iii) the amplitude of the
		PP) on the amplitude and the probability of the novelty response (D); the effects of the baseline on amplitude and probability of the novelty response (E); and the effect of stimulus history on the amplitude and probability of the novelty response (F).
		Amplitude of the novelty response is plotted as a function of the number of local electric organ discharges (LEODs) in the baseline period.
	jeb.biologists.org /cgi/content/full/206/6/999 (7157 words)

	Why Stephen Hawking's Cosmology Precludes a Creator
		A probability amplitude y gives a number that, when squared, is the probability that something exists.
		Contra these authors, what gives the (probable existence of an) idea of a universe is the mathematical probability of there existing an idea of a universe.
		According to Craig, the only probabilities that follow from their model are conditional in the sense that they are transition probabilities for one state of the universe to follow another state.
	www.qsmithwmu.com /why_stephen_hawking's_cosmology_precludes_a_creator.htm (8064 words)

	qureg.C
		We envision our the //description of our register of size "S" as 2^S complex number, //representing the probability of finding the register on one of or //2^S base states.
		Thus if the size of our register is 3 bits array[7] is //the probability amplitude of the state 1,1,1>, and array[7] * //Complex Conjugate(array[7]) = probability of choosing that state.
		Collapse //the state so that the probability of measuring the measured value in //the future is 1, and the probability of measuring any other state is //0.
	alumni.imsa.edu /~matth/quant/299/paper/node41.html (637 words)

	Time-dependent close-coupling calculations of dielectronic capture in He (Site not responding. Last check: 2007-10-18)
		By projecting this wavefunction onto a doubly-excited state of neutral helium, we can determine the probability amplitude for dielectronic capture into one of these states and the subsequent autoionization from it.
		The curve of the maximum probability as a function of the incident energy is in agreement with the Fourier transform of a Gaussian wavepacket with
		One of the nice features of the time-dependent method, is that it allows one to study the formation and decay of autoionizing states as a function of time.
	www.df.uba.ar /users/dmitnik/tdcapture (1988 words)

	OhioLINK ETD: Sadaghiani, Homeyra
		The purpose of this study is to identify students' conceptual and mathematical difficulties in learning the core concepts of introductory quantum mechanics, with the eventual goal of developing instructional material to help students with these difficulties.
		For example, many students confuse the "expectation value" with "probability density" in measurement and some students confuse "probability density" with "probability amplitude" or describe the probability amplitude as a "place" or "area." Furthermore, students' difficulties with the concepts of probability often interfere with their ability to understand and apply the Uncertainty Principle.
		Some students have difficulty with the concept of the wave function as a probability amplitude.
	www.ohiolink.edu /etd/view.cgi?osu1123878116 (401 words)

	[No title] (Site not responding. Last check: 2007-10-18)
		However, in a quantum algorithm the probability vector is comprised of complex numbers.
		The probability of the system residing in any state is given by the square of the absolute value of the amplitude in that state.
		So, a probability vector of [0 1] would indicate a system in the "1" state, a vector of [1 0] could be in the "0" state, and a vector of [1/(2^.5) 1/(2^.5)] would be an even distribution between both states.
	www.nd.edu /~arodrig6/txt/05051518-2001.txt (2211 words)

	baudline manual - histogram
		The unit dBm ranges from +90 dBm, the maximum sample amplitude in 16 bit linear coding space, to -90 dBm, the most negative sample amplitude, with 0 dBm being the origin in the middle.
		This is the probability distribution of the sample amplitudes.
		The sample amplitude scroll bar is on the bottom and the percent of hits scroll bar is on the right.
	www.baudline.com /manual/histogram.html (899 words)

	Interference Effects (Site not responding. Last check: 2007-10-18)
		When the intermediate state of the system is not determined, it is the probability amplitudes for the different intermediate states that must be summed, not the probabilities.
		iii) For a system in a linear superposition of states, the probability amplitude is the sum of the partial amplitude.
		The probability is the square of this sum.
	electron6.phys.utk.edu /QM1/modules/m5/interference.htm (584 words)

	Analysis and Implications of Equivalent Uniform Approximations of Nonuniform Unitary Synaptic Systems -- Uteshev et al. ...
		neurons is often unknown, as are the average probability of release
		is the mean probability of release of each equivalent synapse.
		Note that the partial amplitude distribution function is not determined at zero amplitude, owing to the assumption that the source of transmission failures is strictly presynaptic and not due to any failure in detection.
	www.biophysj.org /cgi/content/full/79/6/2825 (3338 words)

	"Either-Or" Two-Slit Interference: Stable Coherent Propagation of Individual Photons Through Separate Slits -- Alkon 80 ...
		probability amplitude to pass through each of the two slits.
		and is, therefore, the sum of the probability amplitudes for all
		Probability of occurrence of discrete potential waves in the eye of Limulus.
	www.biophysj.org /cgi/content/full/80/5/2056 (3959 words)

	QM: FAQ
		This probability W tells us whether the quantum particle is likely to be in a certain state or location.
		And of course since it is a probability, sometimes you have to measure it lots of times.
		The fact that the average of the momentum is zero doesn't mean the magnitude of the momentum is zero.
	musr.physics.ubc.ca /~jess/p200/qm_faq/qm_faq.html (1248 words)

	Quantum Physics III
		This applet plots the probability amplitude, not the probability density, of the elecron of a hydrogenic atom as a function of the radial distance from the nucleus.
		Notice that for l = 0 the probability amplitude is nonzero at the origin.
		Because this system has spherical symmetry, the probability-amplitude-squared must be multipled by r, the radial coordinate, in order to obtain the probability density.
	www.nhn.ou.edu /~walkup/demonstrations/WebAssignments/QuantumPhysics003E.htm (434 words)

	Double Scattering Experiments (Site not responding. Last check: 2007-10-18)
		Similarly, a probability amplitude that particle a goes to 1 and that at the same time particle b goes to 2 is:
		The probability of finding two identical bosons in an identical final state is twice as large as would be the case for non-identical particles.
		The multiplication of amplitudes for a two-particle system, and their addition or subtraction (as shown above) leads to the following general description of multiplarticle states in quantum mechanics.
	beige.ucs.indiana.edu /B679/node58.html (989 words)

	Converted WP file qutheory
		The value so obtained will give us the probability of obtaining, through measurement on the system, a particular value of the quantity we are interested in.
		The wave function is also called a Probability Amplitude, for this reason.
		Suppose we have a set-up which has equal size slits, located at the same distance from the source of electrons, then the probability that the electron goes through slit number 1 is equal to the probability that it goes through slit number 2.
	www.upscale.utoronto.ca /GeneralInterest/Key/qutheory.htm (1049 words)

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