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There are three aphorisms concerning optimization that everyone should know They are perhaps beginning to suffer from overexposure, but in case you aren't yet familiar with them, here they are: More computing sins are committed in the name of efficiency (without necessarily achieving it) than for any other single reason including blind stupidity William A Wulf [Wulf72] We should forget about small efficiencies, say about 97% of the time: premature optimization is the root of all evil Donald E Knuth [Knuth74] We follow two rules in the matter of optimization: Rule 1 Don't do it Rule 2 (for experts only) Don't do it yet that is, not until you have a perfectly clear and unoptimized solution M A Jackson [Jackson75] All of these aphorisms predate the Java programming language by two decades They tell a deep truth about optimization: It is easy to do more harm than good, especially if you optimize prematurely In the process, you may produce software that is neither fast nor correct and cannot easily be fixed Don't sacrifice sound architectural principles for performance Strive to write good programs rather than fast ones If a good program is not fast enough, its architecture will allow it to be optimized Good programs embody the principle of information hiding: Where possible, they localize design decisions within individual modules, so individual decisions can be changed without affecting the remainder of the system (Item 12) This does not mean that you can ignore performance concerns until your program is complete Implementation problems can be fixed by later optimization, but pervasive architectural flaws that limit performance can be nearly impossible to fix without rewriting the system Changing a fundamental facet of your design after the fact can result in an ill-structured system that is difficult to maintain and evolve Therefore you should think about performance during the design process Strive to avoid design decisions that limit performance The components of a design that are most difficult to change after the fact are those specifying interactions between modules and with the outside world Chief among these design components are APIs, wire-level protocols, and persistent data formats Not only are these design components difficult or impossible to change after the fact, but all of them can place significant limitations on the performance that a system can ever achieve.

Notice that f3n - f3n-1 in (C.85) is the step increment in f3n-l to get to the next term in the series (i.e., f3n). So, in the limit of an infinitesimally small step, the left-hand side of (C.85) becomes an integral. We can anticipate that and approximate (C.85) by

(C.86)

If you had two forms called ProductWin and CommentWin, the resulting usercon g le would look similar to this:

To do the integral on the left-hand side of (C.86), we can change the integration variable from ~ to (with (defined by ~ == tanh(. Then as 1 - tanh 2 ( = sech2( and de = d(sech2(, we find that

(C.87)

<userSettings> <PTWinMyMySettingsProductWin> <setting name="FormLocation" serializeAs="String"> <value>189, 2</value> </setting> <setting name="FormSize" serializeAs="String"> <value>434, 359</value> </setting> </PTWinMyMySettingsProductWin> <PTWinMyMySettingsCommentWin>

U(f3)

.

~~ {1- V 2~arctanhf3}N = exp ( -V~arctanh(3) .

4

(C.88)

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<setting name="FormLocation" serializeAs="String"> <value>50, 140</value> </setting> <setting name="FormSize" serializeAs="String"> <value>184, 190</value> </setting> </PTWinMyMySettingsCommentWin> </userSettings>

Cavity Quantum Electrodynamics: The Strange Theory of Light in a Box Sergio M. Dutra Copyright 2005 John Wiley & Sons, Inc.

The algebra of operators is noncommutative, so that all of the ordinary algebra, calculus, and analysis with ordinary numbers becomes of small utility for operators. Thus, for a single operator, a, ordinary functions of this operator, such as A = exp a, can be defined, for example, by power series. These functions obey the rules of ordinary analysis even though a is an operator. But if another operator 13 is introduced with which a does not commute, the question of functions of the two variables a, (3 is beset with commutation difficulties and the simplest theorems of analysis are lost. For example, if B = exp 13, it is not true that BA, that is exp 13 exp a, is equal to exp(f3 + a). -Richard Phillips Feynman [200]

NOTE: You may still have the old PTWinMyMySettings tag in your user config file You can clear your userconfig files at any time by clicking the Synchronize button on the Settings tab of the Project Designer as shown in Figure 49 This deletes the userconfig files They are recreated the next time you run the application

This is a very useful tool to disentan$le exponentials of certain operato~s ~ften appear in quantum optics.) Suppose that A and B are two operators such that [A, BJ =

more general disentanglement techniques, look at [142,200, 369]

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