Partial Measurement

When we discussed the physics of one quantum particle, we did not explic- 

If the entering particle was in a mixed state (relative to the r-spin measurement), then the act of measurement changes the state of the particle. No one understands how this happens, but it is an essential feature of the quantum mechanical model. For example, this phenomenon contributes to Heisenberg s uncertainty principle, whose most famous implication is that one cannot measure both the position and the momentum of a particle exactly. The point is that a position measurement changes the state of tlie particle in a way that erases information about the momentum, and vice versa. 

In the case of a spin measurement on a single particle, the hnal states are all pure states, without multiplicities. In this case there is only one state corresponding to each possible result of the measurement. But what if the measurement has multiplicities In other words, what if we make only a partial measurement Then there are several states corresponding to one parhcular result of the measurement which state is the hnal state for the measured particle  

To answer this question, we must hrst introduce the quantum mechanical model for measurement. First we discuss measurement on finite-dimensional phase spaces, to avoid mathematical complications. Then we say a few words about the infinite-dimensional case. 

One assumption of the model is that each measurable quantity A (also known as an obser abJe ) of a finite-dimensional quantum system P( V) determines a decomposition of the vector space V into orthogonal subspaces, with a measurement value corresponding to each subspace. In other words, there 

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It is hard for a layman to judge the quality of the various cabinets offered. Much of the quality is hidden beneath the surface and wall not show up until the cabinets have been in use for an extended period of time. Price is only a partial measure of quality. One reason for this is that high style cabinets, offering no more quality or durability than the regular types, demand higher prices. 

Linear transformations that correspond to nonorthogonal matrices distort lengths or angles. The trace and determinant of a matrix provide partial measures of the distortions introduced. 

It is clear that evaporation is superimposed on the electroendosmotic flow and that partial measurements on the open strip account for both phenomena at once (Fig. 12). 

As a partial measure of the quality of the SCF calculations, we compare in Table III calculated and experimental Co-N bond lengths for the and T g species, the ground electronic states for... 

Related to osmotic pressure is osmotic potential. Osmotic potential is a partial measure of a system s free energy. Pure water is arbitrarily assigned an osmotic potential of zero. When a solute is added, the osmotic potential becomes negative. At constant temperature and pressure, water flows from higher osmotic potential to lower osmotic potential. Water potential, another related term, is similar to osmotic potential but takes into account temperature and pressure. Water potential is essentially the same as free energy. When water and the solution in the diagram below have come to equilibrium, points A and B have the same water potential, but the osmotic potential of point B is less than that of point A. 

In Fig. 7, azimuthal current density, JmeiBax, Btr% deduced from magnetization measurement, is presented. As for /m.ax, Jme strongly decreases with the transverse component of the magnetic induction. Jm values, which are an order of magnitude lower than J ax values, are in good agreement with earlier partial measurements... 

Here we assume that the inelastic tnergy du /dt is partially measured. 

Figure 6.10 shows how the permeability of cement paste increases with the tvic ratio. At first it increases slowly and beyond wIc = 0.5 it increases rapidly. The permeability may therefore be regarded as an indirect and partial measure of porosity. Considering the components of cement-based composites it may be assumed that the permeability is determined more by matrix properties than by aggregate ones. Particularly, the matrix/aggregate interface may have the largest content of pores and microcracks which affect the overall permeability (cf. Chapter 7). 

With a required life time of the shaft of 200 000 h, it is not sensible to wait for creep data measured experimentally at comparable times, for this would require about twenty years. To avoid this, data at shorter testing times, which are partially measured at temperatures beyond the service temperature, are extrapolated to larger service times. This is frequently done using the so-called Larson-Miller parameter, moti-... 

The delta of an option instrument measures the extent of this change. A partial measure of the change in the price of an option with respect to a change in the price of the underlying equity is given by the delta, which is... 

Figure 4.83 shows the entry window for the Heavy Liquid section of the Prod Meas. Tab. The measures required for the Naphtha and LCO cuts are routine measurement data. The distillation curve, density, concarbon, sulfur content and nitrogen content are required for all the heavy liquid cuts. In addition, the Olefins, Naphthenes and Aromatics content are required for at least one of the cuts. We must also enter Cloud Point for all LCO type cuts. In most cases, we cannot obtain the distillation curve of the bottoms cut (Routinely not measured or only partial measurement available). Kaes [51] provides a simple correlation to estimate the TBP curve of a bottoms cut as a function of density only. In general, we do not require accurate values for the TBP curve of the bottoms since it is typically not a significant product... 

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