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When the interaction with the electromagnetic field is included, the decay of atomic energy can be understood even in a crude classical model The atom can simply be regarded as an oscillating classical dipole [274} Then the radiation reaction force [314}, which is the force on the atom due to its own field damps the oscillation decreasing the atomic energy This, however, does not explain why there is a stable ground state because such decay would not stop at a minimum energy state but would continue until the collapse of the atom What prevents the collapse We will show in this section that it is the vacuum fluctuations of the electromagnetic field which are responsible for the stability of the ground state.

This will give us insight into the nature of spontaneous emission and will provide us with a picture of the roles of radiation reaction (a classical effect) and vacuum fluctuations (a quantum effect) in this process Our discussion will be based on the approach of Dalibard et al [131} Although the existence of spontaneous emission was pointed out by Einstein [182} the first calculation of the spontaneous emission rate from first principles using quantum electrodynamics was done by Weisskopf and Wigner [631} Our approach in this section retains the crucial assumption of the original Weisskopf-Wigner calculation:.

The Vendors Navigator screen, shown in Figure 2-7, is similar to the Customers Navigator screen discussed in the previous section.

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the Markovian assumption [223]. In the next section we study an example where this assumption breaks down. The hydrogen atom consists of an electron of charge -q and a proton of charge q bound together by their Coulomb intemction. Because the mass of the proton is much larger than the mass of the electron, we can neglect the motion of the former. The problem then reduces to an electron moving under the action of a Coulomb potential. We include the interaction with the quantized electromagnetic field as given earlier:

A measure of the educational infrastructure in biotech is the annual invest ment in tools that support the biological and computer sciences. According to the National Science Board, about 9 percent of the annual budget for the biological sciences is spent on tools such as genomic sequencers, elec tron microscopes, and biological databases. In comparison, about 27 per cent of the educational investment in computer sciences is devoted to infrastructure, predominantly on networks, software, data repositories, and data communications systems. Given the increasing need for academic biological centers to create, maintain, and update vast genomic databases, the National Science Foun dation (NSF) has earmarked the biological sciences as one area in which the infrastructure investments have not kept up with expanding needs and opportunities. This is re ected in a preliminary estimate of NSF future in frastructure needs, based on reports from the NSF directorates and the Of ce of Polar Programs (OPP), as illustrated in Figure 5.13.

q + ~A(r) ]2 + VCoul + Htrans,

The Vendors Navigator screen allows you to access all of the program features and information you need to service and track transactions with your vendors. Functional icons are organized in a convenient owchart format that re ects the chronological order of transactions with your vendor: generating a purchase order, receiving your bill, paying your bill, and so on. If you click the Vendor Detail Center link, you can view a convenient history of your transactions with the Vendor, such as the one shown in Figure 2-8. Just below the Vendor activity links is a menu for accessing vendor reports. And to the left, in the bottom lefthand corner, QuickBooks shamelessly promotes its other convenient services by providing you with links to them. (These services are a credit-checking service and a link to buy more software from Intuit, the makers of QuickBooks.) Similar to the Customers Navigator, this screen contains a plug for QuickBooks services the credit-checking service and a QuickBooks credit card.

(6.1)

(6.3)

Figure 2-8: You can access a vendor history by clicking the Vendor Detail Center link in the Vendors Navigator screen.

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