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The Bethe-Salpeter equation then becomes (4.2.22) To see which terms of the Neumann series for the field covariance are included in the ladder approximation, we iterate (4.2.22) to obtain (4.2.23) Thus under the ladder approximation, the field covariance contains all the "ladder-like" terms. On the other hand, the distorted Born approximation consists of only the first term in (4.2.23).



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Dyson's equation for the mean field and the Bethe-Salpeter equation for the covariance have been derived and are exact equations for the respective statistical quantities. The exact field equations satisfy energy conservation. However, when approximations are imposed upon the Dyson and Bethe-Salpeter equations to the mass and intensity operators respectively, the results may be inconsistent with the requirement of the conservation of energy. Therefore, the question of having approximations on Dyson and Bethe-Salpeter equations that are consistent with energy conservation is an important one. In this section it is shown that the ladder approximation and the nonlinear approximation satisfy energy conservation exactly. The general relation between mass and intensity operators for energy conservation is also established. The consistency in conservation law is derived for the case of real permittivity; that is, both (E) and E are real. f Consider scalar wave in a continuous random medium. The wave equation is





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(V 2 + k 2 )4{r) = _w 2JLE fCr)4J(r)

V ['ljJ*(r)V'ljJ(r) - 'ljJ(r)V'~J*(r)]

(4.2.24)

+ (k 2 -

k*2)'ljJ(r)'ljJ*(r)

In this chapter and the prior one, you have studied line-based patterns: that is, trendlines and channels. Understanding and using these is essential to good charting. But these straight-line patterns are relatively easy to nd, and there are many other kinds of patterns that are important to your knowledge of technical analysis but may not be so obvious. In the next chapter, we will begin this journey into more ambiguous patterns by studying rounded tops and rounded bottoms. These are patterns which can help you predict reversals of a security from which you can pro t.

(4.2.25)

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Equation (4.2.25) is an energy conservation law where the quantity in square brackets defines an energy flux vector, S1/;:

(4.2.26)

-(V 2 + ,,~2)('ljJ(0)) = Q(O, 1) ('ljJ(1)) _(V 2 + k2)(G(0, 1))

(4.2.27) (4.2.28)

= 5(0 -1) + Q(O, 2)(G(2, 1))

('ljJ*(O')'ljJ(O)) = ('l/J*(O'))('l/J(O))

+ (G(O, 1))(G*(0', 1'))1(1,2; 1', 2') (4' (2)'ljJ* (2'))

Two of the most important events that occur repeatedly in technical analysis are breakouts and reversals A breakout is the act of a price escaping from a relatively tight price range either to the upside (a breakout above resistance) or the downside (a failure below support) A reversal is the act of a price changing directly either from (a) up to down, or (b) from down to up What is going on in each case is the same an escape from a price range The terminology differs only to state what has happened prior to that escape Breakouts and reversals are crucial events to discern on a chart since they can make you money, and two of the most common patterns found on charts that relate to these events are rounded tops (at the peak of a chart) and saucers (at the bottom).

(4.2.29)

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