K. Takahashi: "Wigner and Husimi functions in quantum mechanics", J.Phys.Soc.Jap. 55(1986) 762--779 Home/Search Document Not in Database Summary Related Articles Check |
This paper is cited in the following contexts:
The Classical Limit of Quantum Theory - Werner (1995) (Correct)
....functions, or on the limits of coherent states are reviewed. Physics and Astronomy classification scheme PACS (1994) 03.65.Sq, 03.65.Db 1 FB Physik, Universitat Osnabruck, 49069 Osnabruck, Germany 2 Electronic mail: reinwer dosuni1.rz.Uni Osnabrueck.DE 1 1. Introduction The problem of taking the limit of quantum mechanics as h 0 is as old as quantum mechanics itself. Indeed, under the name correspondence principle it was one of the important guidelines for the construction of the theory itself. Naturally, there is a vast literature on the subject, and it requires some ....
....2 it is shown that this furnishes a language in which the convergence of sequences of observables, and the theorems of the 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 ....
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K. Takahashi: "Wigner and Husimi functions in quantum mechanics", J.Phys.Soc.Jap. 55(1986) 762--779
Classical Mechanics as Quantum Mechanics with Infinitesimal h - Werner, Wolff (1995) (Correct)
....) 2 = Gamma h 2 Delta Q 2 ) 2. Then for any A 2 B(H) we define a function on phase space by (S A) hW ( Omega ; AW ( Omega i = h Omega ; ff Gamma (A) Omega i : 6) This is variously called the lower symbol [Sim] a smeared Wigner function [Car] the Husimi function [Tak], or the convolution with a coherent state [We1] of the operator A. In the other direction, we have the upper symbol [Sim] or P representation [KS] also going by many other names) which assigns an operator to each bounded measurable function f via S # f = Z dx dp (2 h) d f(x; p) ff ....
K. Takahashi:"Wigner and Husimi functions in quantum mechanics", J.Phys.Soc.Jap. 55(1986) 762--779
On the Concentration of Quantum States in Phase Space - Werner (1993) (Correct)
....which the statistical interpretation of Quantum Theory is taken seriously, or, on the technical side, whenever norm estimates of states or observables are desired. There is a well known alternative to the Wigner function avoiding these difficulties, which is variously known as the Husimi function [14], a phase space observable [5,7] a Berezin upper lower symbol [13] or convolution with a coherent state [16] One price to pay in all these approaches is that while the Wigner function has an intrinsic characterization in terms of the Weyl operators alone [10] these positive distribution ....
K. Takahashi:"Wigner and Husimi functions in quantum mechanics", J.Phys.Soc.Jap. 55(1986) 762--779
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