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Topic: Expectation values

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Discrete random variable

Poisson distribution

	Expectation Values in Quantum Mechanics (Site not responding. Last check: 2007-10-08)
		Alternatively it could be viewed as the average value of position for a large number of particles which are described by the same wavefunction.
		For example, the expectation value of the radius of the electron in the ground state of the hydrogen atom is the average value you expect to obtain from making the measurement for a large number of hydrogen atoms.
		While the expectation value of a function of position has the appearance of an average of the function, the expectation value of momentum involves the representation of momentum as a quantum mechanical operator.
	hyperphysics.phy-astr.gsu.edu /hbase/quantum/expect.html (198 words)

	More on Expectation Values
		The expectation value of a binomial random variable with N trials and success probability p per trial is N*p.
		This is analogous to an average of the values in a particular data set, except that for computing the average of a particular data set you can take all the values that happen to occur and multiply them by their observed relative frequency (as we discussed in a previous page).
		The average of a lot of squared values should be close to the expectation value of the square.
	www.mathepi.com /stat/prob/expectation2.html (910 words)

	Chap. 11 Examples
		The expectation value of the position variable x, denoted , simply means the average value of the position when repeated measurements are made.
		The fact that the expectation value of is zero for the ground state of the simple harmonic oscillator is not surprising.
		(20) to the case of momentum, we have that the expectation value (or average value) of the momentum is given by
	classweb.gmu.edu /sdavis/chem332/ex11/ex11.htm (2172 words)

	Expected value - Wikipedia, the free encyclopedia
		In probability theory the expected value (or mathematical expectation) of a random variable is the sum of the probability of each possible outcome of the experiment multiplied by its payoff ("value").
		For example, the expected value from the roll of an ordinary six-sided die is 3.5, which is not one of the possible outcomes.
		This estimates the true expected value in an unbiased manner and has the property of minimizing the sum of the squares of the residuals (the sum of the squared differences between the observations and the estimate).
	en.wikipedia.org /wiki/Expectation_value (1198 words)

	Expectation Value Calculations For Game Show "Who Wants To Be A Millionaire"
		The first term is a 50% chance of missing the question and is multiplied by the amount you lose as a result of missing the question.
		The first term is negative and the net expectation value would be zero saying the decisions to go on and try for $64,000 and the decision to stay with the $32,000 would be equivalently desirable from a mathematics standpoint.
		Notice that the expectation value of "Going for the $125,000" is nearly as large as the expectation value of making the "no-brainer." Yet, many people will walk away from this $14,500.
	www.thinkinglike.com /Essays/MillionaireExpectation.html (509 words)

	GENEV : Normalized structure factors (E values)
		One of the factors determining the reliability of E values is the precision of the measured structure factors.
		A squared normalized structure factor is the ratio of its scaled intensity to its expectation value.
		values from 1.0 (the overall mean) indicate whether a reflection is sensitive to the non-random aspects of the structure.
	xtal.sourceforge.net /man/genev-desc.html (2892 words)

	Conservation Laws and Expectation Value Matching
		This equation has an immediate physical interpretation: The change of the expectation value along the characteristics of the particle flow is simply given by the change of the weight along the characteristics of the particle flow because the phase space volume stays constant,
		The emerging finite difference representations of the expectation values along one phase space dimension are then used as prefactors for the finite differencing of terms related to other phase space dimensions in order to build a consistent finite difference representation of the full transport equation.
		Because these canceling terms individually reach large values around and after bounce, this expectation value matching is an essential step for the conservation of energy in the finite difference representation.
	www.cita.utoronto.ca /~liebend/transport/node7.html (956 words)

	S 3.4 Expectation values
		The expectation value of g(x) coincides with the average of a
		The variance V[x] of a random variable is the expectation value of the square of the deviation of the variable from its mean:
		In words: the expectation value of the product of two independent variables is equal to the product of their expectation values.
	www.ph.ed.ac.uk /~alastair/probstats/contents/distributions/expectations/node1.html (670 words)

	Crisp Volume 3 No. 5
		In the standard experimental design of the expectation states program, expectation advantage predicts P(s), the probability that a person will not change an initial choice when informed that a particular other chose the opposite.
		Expectation advantage is used predictively also in studies outside the standard experimental design that involve effects of differential status.
		Values for m (typically about 0.65 for college students), q (typically, 0.10 < q < 0.15), and the path lengths should be entered.
	www.uiowa.edu /~grpproc/crisp/crisp.3.5.htm (1126 words)

	[No title]
		REGEM % returns % % X, the data matrix with imputed values substituted for NaNs, % M, the estimated mean of X, % C, the estimated covariance matrix of X, % Xerr, an estimated standard error of the imputed values.
		First, for each record X(i,:) with % missing values, the regression parameters of the variables with % missing values on the variables with available values are % computed from the estimates of the mean and of the covariance % matrix.
		Second, the missing values in a record X(i,:) are filled % in with their conditional expectation values given the available % values and the estimates of the mean and of the covariance % matrix, the conditional expectation values being the product of % the available values and the estimated regression % coefficients.
	www.gps.caltech.edu /~tapio/imputation/regem.m (663 words)

	Calculation of expectation values
		The closed time path formalism codifies the causal relationship between source and response, for the computation of expectation values in a general mixed state.
		That the CTP generator leads to a causal result is easily verified by realizing that the expectation value of the field is always coupled to the sources by the retarded n point functions.
		The desired expectation value is therefore manifestly real and causal, and the time dependence since the initial time is contained entirely in the
	www.iu.hio.no /~mark/physics/noneq/node9.html (502 words)

	RFC2616 -- 14 Header Field Definitions -- Page 2
		Comparison of expectation values is case-insensitive for unquoted tokens (including the 100-continue token), and is case-sensitive for quoted-string expectation-extensions.
		If the last-byte-pos value is absent, or if the value is greater than or equal to the current length of the entity-body, last-byte-pos is taken to be equal to one less than the current length of the entity-body in bytes.
		The Vary field value indicates the set of request-header fields that fully determines, while the response is fresh, whether a cache is permitted to use the response to reply to a subsequent request without revalidation.
	256.com /gray/docs/rfc2616/14-2.html (7037 words)

	Expectation - Wikipedia, the free encyclopedia
		For expectation in the context of probability theory and statistics, see expected value.
		An expectation, which is a belief that is centred on the future, may or may not be realistic.
		An expectation about the behavior or performance of another person, expressed to that person, may have the nature of a strong request, or an order.
	en.wikipedia.org /wiki/Expectation (209 words)

	Chi-Square Bias in Runs-Up/Down RNG Tests
		When (pseudo) random number generators (RNGs) are tested under a "runs up" or "runs down" test, the expectation values described in Knuth II may not be appropriate.
		Those expectation values seem designed for RNG's which produce a huge number of different values, and are not accurate for RNG's which generate only a small population of values.
		Based on this data, one is forced to conclude that the experimental run length values match the counting values typically 100x better than the alternative.
	www.ciphersbyritter.com /ARTS/RUNSUP.HTM (1692 words)

	The Faustmann Symposium
		The lack of calculations of land expectation values with consideration of the risk of stand damages in Germany might be especially due to missing information about the natural risk of forest stands.
		Land expectation values with consideration of the risk of natural stand damage are computed in a simulation model on basis of these probabilities.
		The results of the simulations are assessed by the expected value of land expectation value and by its dispersions.
	www.lsu.edu /faculty/sjchang/abs042.htm (435 words)

	The Superposition State Introduced (Site not responding. Last check: 2007-10-08)
		The expectation value of any observable in this system corresponds to the average of a large number of measurements on identically prepared systems.
		This is why the energy eigenstates of the system are called stationary; The expectation values in these states are all constant.
		Or, the expectation value of this 50-50 superposition state of the stationary states with n=1 and n=2 is the average of the expectation value in each of those states PLUS a term that oscillates in time at the frequency that corresponds to the energy difference between those two stationary states divided by (h
	itl.chem.ufl.edu /3417_s98/lectures/super_1.html (380 words)

	Choice of Basis Vectors
		The sequence of taking the averages is significant, the quantum average being taken separately for each state, the various quantum averages then being combined to yield a thermal average.
		After the expectation value has been evaluated separately for each element of the quantum ensemble, the thermally weighted statistico-mechanical average of
		A first question is whether or not we were justified in using the list of energy eigenstates of the system as a correct list of all states of the system.
	users.wpi.edu /~phillies/stat11/node1.html (872 words)

	Dirac-Fock using different nuclear charge distributions
		In this parametrization the exponential parameter, xi, is obtained by equating the RMS value of the Gaussian radial distribution to the empirical formula in Eq.
		Spinor energies and radial expectation values of the spinors that were calculated using the different models for the nuclear charge distribution are available as supplementary data.
		This table gives the radial expectation values of r of the orbitals calculated using four different nuclear models.
	dirac.chem.sdu.dk /doc/FiniteNuclei/FiniteNuclei.shtml (1968 words)

	Quantum mechanics postulates
		Suppose the wavefunction associated with a definite quantized value (eigenvalue) of the observable is denoted by
		(see basis set postulate), so the operator Q can be used to extract a linear combination of eigenvalues multiplied by coefficients related to the probability of their being observed (see expectation value postulate).
		The function can be represented as a linear combination of eigenfunctions of Q, and the results of the operation gives the physical values times a probability coefficient.
	hyperphysics.phy-astr.gsu.edu /hbase/quantum/qm2.html (402 words)

	Students > Values & Expectations :: Avondale ::
		The following expectations have grown out of Christian values, beliefs and Adventist traditions, and are set out here so that students are aware of the values and expectations held by the College.
		In valuing excellence in learning and teaching the personal and professional growth of staff is also highly valued.
		Avondale College values integrity in its own operations and it seeks to develop skilled graduates who will act with integrity and ethical principles in their future personal and professional lives.
	www.avondale.edu.au /students/values (678 words)

	Expectation values and mean square deviations
		Yeah, I am unsure because I always thought that the expectation value of let's say was the integral of the wave functions squared multiplied by x.
		There is a distinction between theoretical values, which can be computed directly, and statistical values.
		The statisitcal value is obtained by running lots of trials and averaging the results by the number of trials.
	www.physicsforums.com /showthread.php?t=42830 (475 words)

	allometra \| blast parser
		normalized expectation value reflects the absolute value of the exponent in the expectation value.
		If the expectation value is 2e-15, the normalized expectation value is 15.
		For all expectation values better than e-100, like 3e-101, 7e-156, etc., the normalized expectation value 100 is assigned.
	www.allometra.com /blast_parser.shtml (1001 words)

	8.13 One-electron operators and expectation values (GEXPEC)
		The operators for which expectation values are requested, are specified by keywords on the global
		card, expectation values are computed in all subsequent programs (if applicable).
		Expectation values are only nonzero for symmetric operators (parity=1).
	www.chm.tu-dresden.de /edv/manuals/molpro2000/manual/node65.html (148 words)

	One-electron expectation values: *EXPECT
		Invokes the calculation of the one-electron contribution to the magnetizability expectation value.
		Set the number of integration points to be used in the Gaussian quadrature when evaluating the diamagnetic spin-orbit integrals.
		Invokes the calculation of the one-electron contribution to the nuclear shielding expectation values.
	www.kjemi.uio.no /software/dalton/manual/node151.html (376 words)

	Expectation Values (Site not responding. Last check: 2007-10-08)
		Suppose we make a large number of measurements to determine a property, such as the position or the momentum, of an object.
		To determine the average value of that property, we would add up all of the values we had obtained and divide by the number of measurements.
		The most general expression to determine the expectation value for a particular quantity is given by
	www.usd.edu /phys/courses/phys431/notes/qmnotesa.htm (155 words)

	The calculation of the expectation values of the physical quantities involves an application of quantum-mechanical ...
		The calculation of the expectation values of the physical quantities involves an application of quantum-mechanical methods.
		Many of such methods include the calculation of the commutators consisting from the operators of the appropriate physical quantities.
		The development of such program is the main goal of the project.
	www.public.iastate.edu /~kohutyuk/AIwebsite/try.htm (248 words)

	Experiment Results
		This value is clearly in violation of the hidden variable prediction and corresponds almost exactly to the quantum mechanical description!
		In addition to this result, a plot of the experimental expectation values verses the angle between the two detector orientations is given below.
		Quantum Mechanics has predicted not only the correct value for S but also the correct dependance of the expectation value on the detector angles.
	roxanne.roxanne.org /epr/results.html (484 words)

	Pure States
		i.e., the average of expectation values associated with states
		Note that such an expectation value is not only determined by the average of expectation values associated with states k (i.e., the first term in the r.h.s of Eq.
		of such a pure state will coincide with the expectation values given by the equations Eq.
	xbeams.chem.yale.edu /~batista/vaa/node3.html (222 words)

	Expectation values
		What is the mean value of the measurement?
		This quantity, which is generally referred to as the expectation value of
		Thus, the expectation value of this operator is always unity: i.e.
	farside.ph.utexas.edu /teaching/qm/lectures/node14.html (112 words)

	[No title]
		One of the most important tools in the use of quantum mechanics is the calculation of ‘expectation values’ of quantum mechanical observables- quantities which can be measure experimentally.
		The appropriate ground state wavrfunction for this electron as we’ve seen in class is: (where L is the length of the box) EMBED Equation.3 We’ll see where this came from later in the class.
		If you know the value for L, the width of the box and the point a at which you are evaluating the momentum operator then you can calculate the momentum at that point, right?
	faculty.une.edu /cas/cnash/EVs.doc (850 words)

	Case 1: Functions only of momentum
		Now, we see that the expectation value can be obtained by evaluating all the coordinate space matrix elements of the operator and all the coordinate space matrix elements of the density matrix.
		A particularly useful form for the expectation value can be obtained if a momentum space identity is inserted:
		Despite its compelling appearance, the evaluation of expectation values of functions of momentum are considerably more difficult than functions of position, due to the fact that the entire density matrix is required.
	www.nyu.edu /classes/tuckerman/stat.mech/lectures/lecture_17/node3.html (275 words)

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