V. P. Maslov and M. V. Fedoriuk: Semi-Classical Approximation in Quantum Mechanics , D. Reidel, Dodrecht, (1981).  Home/Search   Document Not in Database   Summary   Related Articles   Check

....and no 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 ....

....the action S : IR d IR. The distribution of position in these vectors is j (x)j 2 , independently of h, and the rapidly oscillating phase determines the momentum. Asymptotic estimates of expectation values in such states 19 are traditionally evaluated using the stationary phase method [Mas] Since this typically involves some partial integration, the technical conditions in such results usually demand some smoothness of and S. In our context we can get by with the minimal assumptions needed to even state the asymptotic formula. 13 Theorem. Let 2 L 2 (IR d ) with k k = 1, ....

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V.P. Maslov and M.V. Fedoriuk: Semi-classical approximation in quantum mechanics, D. Reidel, Dordrecht 1981

....D 49069 Osnabruck, Germany E mail: reinwer dosuni1.rz.uni osnabrueck.de ( Math. Institut, Univ. Tubingen, Auf der Morgenstelle 10, D 72076 Tubingen, Germany E mail: manfred.wolff uni tuebingen.de 1 Introduction The classical limit of quantum mechanics is often identified with the WKB [Mas, BS] method. While this approach gives a good picture of the asymptotic behaviour of solutions of the Schrodinger equation as h 0, it does not give a satisfactory explanation why in this limit the non commutativity of quantum observables suddenly turns into the commutativity of classical ....

V.P. Maslov and M.V. Fedoriuk: Semi-classical approximation in quantum mechanics, D. Reidel, Dordrecht 1981

....the same as that provided by quantum perturbation theory. Recently, there has been considerable renewed interest in the various aspects of the Semi Classical Approximation (SCA) a powerful motivation behind that being the problem of the so called quantum chaos (see for example references [1,2,3,4,5]) An important aspect is represented by the quantum energy levels, and in this connection one recent work [6] shows that the predictions of individual levels by SCA (by this we mean the Bohr Sommerfeld formula, or one of its generalizations to the non integrable case, such as EBK; see e.g. ....

V.P. Maslov and M.V. Fedoriuk: Semi--Classical Approximation in Quantum Mechanics (Reidel Publishing Company, 1981)

....0 e S yields the Einstein Brillouin Keller (EBK) quantization conditions ; n j 2 Z ; 13) where fC j j j = 1; dg denotes a basis of noncontractible loops on the torus characterized by the action variables I j = pdx. The number j 2 f1; 2; 3; 4g is the Maslov index, see [13], of the cycle C j which, roughly speaking, counts the number of points along C j at which the pre factor x becomes singular. All these terms also appear in the situation with non zero spin, and we now have to examine how the spin contribution modi es this picture. When we include the spin ....

V. P. Maslov and M. V. Fedoriuk: Semi-Classical Approximation in Quantum Mechanics , D. Reidel, Dodrecht, (1981).

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