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Born-Oppenheirner Approximation For bound states involving heavy quarks such as bb or c the quark masses are sufficiently large that nonrelativisC tic quantum mechanics and potential descriptions may be formally justified (5126) For a bag description of such states a Born-Oppenheamer or adiabatic approximation may be appropriate Recall that the Born-Oppenheimer approximation in molecular physics assumes that the electrons move much more rapidly than the nuclei, so that in molecules the electrons follow the motion of the nuclei adiabatically If it is assumed that the gluon fields and bag boundaries move quickly relative to the motion of the heavy quarks, the bag problem can be solved in two steps: (1)the quarks are fixed in space at positions ri and the gluon field and bag boundary resulting from the fixed sources are calculated, yielding the energy as a function of quark positions E(r1,r2, .

FIGURE 8.2 Converting layers into a Smart Object. Select the layers (left), and choose Layer Smart Objects Convert to Smart Object. The Smart Object replaces the layers in the Layers palette (right).

); (2) the energy calculated in the first step is used as a potential energy in a Schrijdinger equation for the quark motion (see, eg, Heller, 1982) In this approximation the bag develops naturally around the quarks, the potential depends only on the relative coordinates ri - rj, and we do no violence to the translational invariance This is not true for the bag model with light quarks, where one expects the quark motion t o be too fast for the Born-Oppenheimer approximation There the bag is first specified, then the quarks are fed into it; this guarantees a violation of translational invariance, with attendant spurious modes associated with motion of the center-of-mass The heavy-quark bound states are well described by nonrelativistic potentials and they will be discussed later in that context (5126).

All I want to leave behind is a committed life. King valued a committed life, a life dedicated to changing human rights. What do you value most These may include money, civil rights, creating a useful product, helping the homeless, or other values such as creating a better world or a better environment for our children. List 10 of your key values. Now here is the kicker. Pick two or three careers (or different jobs within your current career path) that you think are in line with your true vision. Write a persuasive paragraph for each career, as if you were writing to a friend, and tell this friend how your purpose statement and values are aligned with this particular career. The paragraphs that are dif cult to write, that is, the careers that had to be bent and pushed to t into your statement and values, are probably not a good choice. This career choice is out of sync with your true vision. On the other hand, the paragraph that was the easiest to write, the one that was the best t for your purpose and values, will be the correct choice and a step toward following your vision. Henry David Thoreau once stated, In the long run, men hit only what they aim at. I would add We need to know where to aim. This chapter will point you in the right direction.

first time, there is a tendency to view everything as an agent. This is perceived to be in some way conceptually pure. But if one adopts t h s viewpoint, then one ends up with agents for everythng, including agents for addition and subtraction. It is not difficult to see that naively viewing everything as an agent in this way will be extremely inefficient: the overheads of managing agents and inter-agent communication will rapidly outweigh the benefits of an agent-based solution. Moreover, we do not believe it is useful to refer to very fine-grained computational entities as agents.

However, we observe here that in a bag description the short-range potential is Coulombic ( l / ~ while at larger separations the bag forms flux tubes that generate a ), linear potential (constant force) This was anticipated in our previous discussion..

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If you want to use the still picture elsewhere in Mac OS X, Ctrl-click or right-click the picture s clip on the Storyboard and choose Reveal in Finder. iMovie opens a Finder

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This is a representation of how the line is stored in the AutoCAD drawing database. AutoLISP returns a large list that contains multiple smaller lists. Each of the smaller lists is referred to as a group indexed by the first element. The entity name is in group 1. Each of the initial numbers in the small lists represents a different quality of the line. These numbers are called object group codes. The object group codes used most often are listed in Table 35.2. TABLE 35.2