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As can be seen from (6.3), we have neglected the constant self-energy contribution to the Coulomb energy. This term leads to a shift in the mass of the bare particle. It is the same mass renormalization as that present in classical theory [131]. The linear size of a typical hydrogen atom is on the order of 1A. Only x-rays have wavelengths of that magnitude. The wavelengths of electromagnetic radiation emitted and absorbed by electronic transitions are usually much longer than this. When such radiation interacts with the atom, the field experienced by the electron is, to a very good approximation, the same experienced by the nucleus. So in equation (6.1) we can replace the position operator of the electron, r, in the argument of A by the position of the proton, which we assume fixed at the origin. This is called the dipole approximation (see Sec. 5.1). In the electric dipole approximation, the electron is insensitive to the magnetic field and the Heisenberg equation for the Cartesian momentum 7r= p + (qj c)A(O) together with the Heisenberg equation for the position of the electron (i.e., r =7r jm) yields the Newton-Lorentz equation without the magnetic force term

The United States bene ts from the presence of students and scientists from Asia, Europe, and other countries who work in U.S. university research laboratories. In return, when these highly skilled scientists return home, they contribute to their native country s education and research and devel opment infrastructure. The National Science Foundation reports that there was a 4 percent increase in the number of students enrolled in graduate science and engi neering programs from 2000 to 2001, and much of this increase was due to an increase in students with temporary visas. Enrollment increased 9 percent, with the greatest increases in engineering and computer sciences. In 2001, students with temporary visas made up half of graduate students in computer sciences and engineering. The distribution of U.S. doctorates awarded temporary visa holders is shown in Figure 5.14. Of note is that about 15 percent of the doctorates awarded were in the biological sci ences. About four times the number of doctorates were awarded in the bi ological sciences to temporary visa holders than were awarded in the computer sciences. Students in search of training are not only more mobile, but as gradu

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a~(k)

The Employees Navigator screen, shown in Figure 2-9, is the human resources department of QuickBooks. It contains an icon section to access program features for tracking time, payroll liabilities, and payments to employees. The Related Activities section contains links that allow you to launch speci c tasks relative to managing your employees. The Memorized Reports section, in the lower right corner of the screen, offers drop-down menu access to employee and payroll reports. This screen also contains links to access information about additional payroll management services offered by Intuit for a fee.

- VVCoul - qE-t.(O).

(6.4)

170 OPP 6%

-iwa~(k) - i q j,Ao(k) (k). 7r,

The Banking Navigator screen, shown in Figure 2-10, has icons that allow you to access portions of the QuickBooks program used to write checks, make deposits, and perform other banking functions. The Related Activities section allows you to launch speci c tasks such as printing checks and pay stubs and sending payroll data to Excel. The Memorized Reports section permits you to access customer, vendor, and other lists. For example, you can view a detailed summary of information about all checks you have written, as shown in Figure 2-11. You can also view a separate report summarizing deposits you have made, similar to the one shown in Figure 2-12.

(6.5)

Ao(k)

The Business Services Navigator, shown in Figure 2-13, is a catalog of useful additional products and services you can purchase from Intuit. You can purchase checks, supplies, and payroll services or sign up for a QuickBooks credit card for your business using this Navigator screen.

SBE 3% BIO 20%

We can integrate equation (6.5),

(6.6)

Even if you are not a Help enthusiast because the Help features in other Windows programs have disappointed you, continue to read this section. You ll nd some of the QuickBooks Help features to be truly useful.

a~(k, t) = a~(k,O)e-iwt -

q j,Ao(k) ft dt' e-iw(t-t') (k). 7r(t').

MPS 24% CISE 15%

(6.7)

Similar to other Windows programs, QuickBooks contains a standard Help menu that can be accessed from the taskbar at the top of the QuickBooks window, as shown in Figure 2-14. You can resize and move the Help window. Use the tile option in the upper right corner of the screen to reduce the size of the Help window. Simply click the border until a double arrow appears and then drag the Help window to where you want it.

Let us write the vector potential as a sum of two terms: A(O, t) = Avac(O, t) where the first term is the vacuum part: Avac(O,t) =

+ As(O, t),

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