B. Helffer: Semi-classical analysis for the Schrodinger operator and applications, Springer Lect.Not.Math. 1336, Berlin 1988  Home/Search   Document Not in Database   Summary   Related Articles

....desired type can be adequately expressed. The definition of the comparison maps j hh 0 requires some additional structure from phase space quantum mechanics, and is undertaken in Section 3. Section 4 gives an extensive list of examples and applications. We hope that this section especially will help to convince the reader that the present approach to the classical limit is a natural, if not canonical one. Section 5 contains the more technical aspects, including, of course, the proofs of the main results. Some of these technical points, notably the proofs of the theorems about convergence of ....

....attempt has been made to evaluate the historical development of the subject, or to decide any priority claims. Nor can we adequately portray the merits of the different schools since our perspective is limited to the comparison with the approach of the present 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 ....

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B. Helffer: Semi-classical analysis for the Schrodinger operator and applications, Springer Lect.Not.Math. 1336, Berlin 1988

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