![]() | This article is rated C-class on Wikipedia's
content assessment scale. It is of interest to the following WikiProjects: | ||||||||||
|
The following reference was deleted today:
M. Oliva, D. Kakofengitis, and O. Steuernagel (2018). "Anharmonic quantum mechanical systems do not feature phase space trajectories". Physica A. 502: 201–210.
doi:
10.1016/j.physa.2017.10.047.{{
cite journal}}
: CS1 maint: multiple names: authors list (
link) Apparently, to me, in excessive overprotective zeal. While I have not met the authors, I and several respected colleagues have internalized the rather natural lessons therein, and the diffidence ("must wait") in the comment box of said deletion is unwarranted, in my opinion. Nevertheless, here it is, for access by the motivated editor and, of course, posterity of good sense.
Cuzkatzimhut (
talk)
23:00, 15 November 2018 (UTC)
This interesting paper is about trajectories, which appear in the argument of the Wigner function. In Eq. (19) we see the dot-composition of two functions W(q(x,t)) in the sense of mathematical analysis. The wiki article discusses star-product trajectories that also appear in the argument of the Wigner function. The resultant object is, however, the star-composition of two functions W(*q(x,t)). Readers would be grateful if somebody wrote a section on why the dot- and star-product trajectories as well as the de Broglie Bohm trajectories are pairwise different. It is clear that objects related to the dot-composition of functions do not belong to the Moyal dynamics. I am not surprised therefore by the inconsistencies that arise when replacing W(*q(x,t)) -> W(q(x,t)). Mr Renovator ( talk) 13:49, 20 November 2018 (UTC)
The average value of the operator Ĝ can be expressed in terms of the Wigner function in two ways. The first method uses the completeness property of the basis B(ξ) with respect to the density matrix ρ and the operator Ĝ:
where
From other hand, the completeness property with respect to the product of the operators ρ and Ĝ means
where conditions are taken into account
We thus conclude
For a family of Wigner functions tending to zero at infinity together with all their derivatives, integration in parts proves this equality in an independent way (cf. Lemma 2 of Ref. [5] in the Wigner–Weyl transform), entering, oddly enough, into contradiction with the footnote 19 on page 71 of the textbook "Lectures on Quantum Mechanics for Mathematics Students" (Student Mathematical Library) L. D. Faddeev and O. A. Yakubovskii (American Mathematical Society, 2009). When calculating the average, star-product can also be omitted in the Glauber–Sudarshan P representation and the Husimi Q representation. -- Edehdu ( talk) 06:19, 6 May 2022 (UTC)
![]() | This article is rated C-class on Wikipedia's
content assessment scale. It is of interest to the following WikiProjects: | ||||||||||
|
The following reference was deleted today:
M. Oliva, D. Kakofengitis, and O. Steuernagel (2018). "Anharmonic quantum mechanical systems do not feature phase space trajectories". Physica A. 502: 201–210.
doi:
10.1016/j.physa.2017.10.047.{{
cite journal}}
: CS1 maint: multiple names: authors list (
link) Apparently, to me, in excessive overprotective zeal. While I have not met the authors, I and several respected colleagues have internalized the rather natural lessons therein, and the diffidence ("must wait") in the comment box of said deletion is unwarranted, in my opinion. Nevertheless, here it is, for access by the motivated editor and, of course, posterity of good sense.
Cuzkatzimhut (
talk)
23:00, 15 November 2018 (UTC)
This interesting paper is about trajectories, which appear in the argument of the Wigner function. In Eq. (19) we see the dot-composition of two functions W(q(x,t)) in the sense of mathematical analysis. The wiki article discusses star-product trajectories that also appear in the argument of the Wigner function. The resultant object is, however, the star-composition of two functions W(*q(x,t)). Readers would be grateful if somebody wrote a section on why the dot- and star-product trajectories as well as the de Broglie Bohm trajectories are pairwise different. It is clear that objects related to the dot-composition of functions do not belong to the Moyal dynamics. I am not surprised therefore by the inconsistencies that arise when replacing W(*q(x,t)) -> W(q(x,t)). Mr Renovator ( talk) 13:49, 20 November 2018 (UTC)
The average value of the operator Ĝ can be expressed in terms of the Wigner function in two ways. The first method uses the completeness property of the basis B(ξ) with respect to the density matrix ρ and the operator Ĝ:
where
From other hand, the completeness property with respect to the product of the operators ρ and Ĝ means
where conditions are taken into account
We thus conclude
For a family of Wigner functions tending to zero at infinity together with all their derivatives, integration in parts proves this equality in an independent way (cf. Lemma 2 of Ref. [5] in the Wigner–Weyl transform), entering, oddly enough, into contradiction with the footnote 19 on page 71 of the textbook "Lectures on Quantum Mechanics for Mathematics Students" (Student Mathematical Library) L. D. Faddeev and O. A. Yakubovskii (American Mathematical Society, 2009). When calculating the average, star-product can also be omitted in the Glauber–Sudarshan P representation and the Husimi Q representation. -- Edehdu ( talk) 06:19, 6 May 2022 (UTC)