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FIGURE 4-8

expect for a vibrating string, except a system that resembles a harmonic oscillator. Let s continue forward. Since [ m , n ] = m m+n ,0 , we can write

CHAPTER 2: Blast-Off!

uses another object (the proxy) to act as a stand-in for the real object. The proxy creates the implementation object only if the user requests it. An example of the proxy pattern implemented in JEE is the EJB remote interface.

(4.13)

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The Decorator pattern provides the same contract for a class but with extended functionality. The pattern is used when functionality needs to be added to objects dynamically. The solution involves encapsulating the original object inside an abstract wrapper interface. Both the decorator objects and the base object inherit from this abstract interface. The interface is generic such that it allows a theoretically unlimited number of decorative layers to be added to each base object. Decorators would seem to be especially useful when you wish to add functionality when you do not have the actual code source of the class. If you know enough about the object that is, the interface when you want to decorate, you can provide a decoration for it. It is important to note that the decorator is a subclass of the component class that it decorates. This is counterintuitive because the instance is a parent of the component it decorates. Decorators share the wrapper approach. The difference, however, is intent. The decorator has value only if it changes the behavior of the wrapee. The EJBObject is a decorator for the bean because the bean s functionality is expanded to include remote behavior.

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At this point, it is important to take a step back and recognize a key fact. The commutation relation not only bears some resemblance to the harmonic oscillator of quantum mechanics, but there is a very important difference. Notice that the presence of the metric means that we can have negative commutators. This is the case for the time components. That is, since 00 = 1, it follows that

The Factory Method pattern (as shown in Figure 4-9) provides the ability to define an interface for creating an object but defers instantiation to subclasses. JEE technology uses this pattern for the EJBHome interface, which creates new EJBObjects. (For more information, see 5 and perhaps consult the book Design Patterns: Elements of Reusable Object-Oriented Software by Erich Gamma, Richard Helm, Ralph Johnson, and John Vlissides [Addison-Wesley, 1995].)

Figure 2 24. Open the Classes folder and click on the RootViewController.m file to examine the pre-existing boilerplate code.

This is going to turn out to be important because it can lead to negative norm states. Now, in analogy with the harmonic oscillator from ordinary quantum mechanics, we de ne a number operator. These are given in terms of the modes as Nm = m m where we take m 1. The eigenstates of the number operator satisfy N m im = i m im The total number operator is de ned by summing over all possible N m = m m: N = N m = m m

FIGURE 4-9

The Abstract Factory pattern provides an interface for creating families of related or dependent objects without specifying concrete classes. JEE technology uses this pattern for the EJBHome interface, which creates new EJBObjects.

(4.14)

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