L. Hormander: The analysis of linear partial differential operators, ?? volumes Springer, Berlin 1985  Home/Search   Document Not in Database   Summary   Related Articles

....In this interpretation a limit theorem says that the classical treatment is accurate (within certain bounds) as long as the relevant observables change sufficiently slowly relative to the phase space scale fixed by h. The introduction of a changeable parameter h is then merely a convenient shorthand for this comparison. What makes it especially convenient is that the comparison parameter h will show up in all those places, where we are used to seeing the constant h in the textbooks. 2 For the mathematical formulation of the classical limit both readings amount to the same thing. The ....

....paper. A) The WKB method. Mas,Sch,Hel,Fro,DH,BS] One virtue of this well known approach is that it is so close to Schrodinger s beautiful series of papers establishing his wave mechanics. It fails mainly on item (a) the Schrodinger equation is only one aspect of quantum mechanics, and its short wave asymptotics is only one aspect of the classical limit. For example, it seems hopeless to try to understand the opera3 tor properties (e) and (f) in WKB terms. The WKB wave functions do correspond to (a subclass of ) convergent states in our approach (see Section 4.8) Their limits are ....

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L. Hormander: The analysis of linear partial differential operators, ?? volumes Springer, Berlin 1985

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