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We can define 'l'fgh' etc., in a similar manner. At very low temperatures the wa\e function of the liquid is an incoherent superposition of all such wave functions. with different numbers of wave packets (incoherent, because we are considering a quantum ensemble). The coefficients in this superposition depend on the temperature, in such a manner that the average number of excitations of approximate wave vector k is (n k ). In this ensemble, the factor '1'0 in (13.24) and (13.25) is the same for all waw functions, as long as (nk)/N 1. Thus, at a finite but small temperature, the superfluid continues to be represented by the ground state wave function '1'(1. while the normal fluid is the gas of elementary excitations. Near absolute zero, then, the normal fluid component of liquid helium consists of a very dilute gas of elementary excitations, in the form of phonons. Landau argues that at such low temperatures, He II can flow past a wall without function, as long as the flow velocity is less than c. To understand this we need only consider what happens if an external object with a velocity ve is dragged through a stationary liquid. Since the only excitations of the liquid are phonons, the only ways energy and momentum can be imparted to the liquid are by (a) excitation of new phonons and (b) scattering of existing phonons. Suppose an amount of energy 6. is transferred through excitation of a number of phonons, specified by the occupation numbers {n k }:

(13.26)

6.P =

(13.27)

(13.28)

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stock. Figure 5.27 shows the popular NASDAQ ETF (symbol QQQQ) with four different RSI signals: three of them sells, and one of them a buy. In this example, each of these signals correctly anticipated the future direction of the stock. Stocks with RSI studies that are moving steadily without an abundance of signals are typically the most pro table. Figure 5.28 illustrates such a case with United States Steel (symbol X). In late October, after a steady decline in prices, the RSI pushes above the 30 level and anticipates a handsome 40 percent appreciation in the stock within a very short time period. The RSI slips beneath the 70 level in early December, providing for an easy opportunity to lock in pro ts before the stock eases in price any more. This chapter has given you an introduction to the basic concepts behind technical indicators. Although we have examined just a few basic studies, you should at this point understand: The difference between overlaid and independent indicators. Principles behind interpreting buy and sell signals with studies.

(13.29)

To print a report from Print Preview view, click the Print Preview tab and click the Print button. Alternatively, click the File button and click Print to open the Print dialog box, where you can select various printing options.

(13.30)

This is impossible unless Ivel > c. At low temperatures the transfer of energy and momentum through scattering of existing phonons can be neglected because as T ~ 0 the number of phonons becomes zero. It is noted that the argument depends on the linearity of the phonon energy spectrum and does not apply to an ideal gas of bosons. The foregoing argument is valid at absolute zero, but it breaks down at a higher temperature when there are many phonons present. The external object may now transfer energy and momentum by scattering the phonons. Experiments on the flow of He II past a wall at 1 K indicate that the critical velocity is orders of magnitude smaller than c.

(13.31)

The total momenta of these states come exclusively from the elementary excitations (the normal fluid), while the superfluid remains uniform and stationary. It is clear that there are states not included above in which the superfluid also contributes to the total momentum. Such states become important if we want to describe the flow of the superfluid. To generate the states for which the superfluid is flowing uniformly, all we have to do is to multiply the ground state wave function, which is a common factor to all the states we are considering, by exp (i P Rill) where P is the total momentum and R the center-of-mass coordinate:

(13.32)

The new ground state wave function corresponds to a superfluid moving uniformly with velocity Vs = P INm. In a frame moving with the superfluid, all

(13.331

FIGURE 5.28 The RSI is easiest to use on broad, more gradual movements,

1i 2

LV} + L u(lri - r;l)

Outlook is a personal information manager for the computer desktop. You can use Outlook s Calendar component to manage appointments in your calendar; its Contacts component to keep track of contacts; its Tasks component to organise lists of tasks you need to complete; its Mail component to send and receive e-mail messages; and more. You can perform a wide variety of everyday tasks from the Outlook window. In this part, you learn how to put Outlook to work for you using each of the major components to manage everyday tasks.

= --:-

(13.34 )

Under the Galilean transformation they become*

(13 .35)

k.'0

k)n k + ~Nmu; (13.36)

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