Timeline for Representing a rotation around an arbitrary axis using Wigner $D$-matrix
Current License: CC BY-SA 4.0
18 events
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| Jul 26, 2022 at 22:03 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Mar 27, 2022 at 1:03 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Nov 24, 2021 at 13:04 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Jul 19, 2021 at 18:02 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Mar 20, 2021 at 3:03 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Oct 7, 2020 at 3:00 | history | tweeted | twitter.com/StackPhysics/status/1313675592315920384 | ||
| Oct 6, 2020 at 16:50 | history | edited | Qmechanic♦ | CC BY-SA 4.0 |
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| Oct 6, 2020 at 16:27 | answer | added | ZeroTheHero | timeline score: 2 | |
| Oct 6, 2020 at 15:39 | comment | added | Voulkos | Related : My answer here Euler Rotations in Ordinary Space. I think that equating the expression $\mathrm{A}\left(\psi,\theta,\phi\right)$ of equation (01) to the expression $\mathrm{A}\left(\mathbf{n},\Phi\right)$ of equation (03) of my answer you will find the vector $\sin\Phi\mathbf{n}$ in terms of the Euler angles $\left(\psi,\theta,\phi\right)$. | |
| Oct 6, 2020 at 15:18 | history | edited | Qmechanic♦ |
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| Oct 6, 2020 at 14:43 | comment | added | Cosmas Zachos | Well, draw the picture. You effectively rotated by π around n in pictorial terms. This does not amount to a reflection in the fixed axis system, rightly so. | |
| Oct 6, 2020 at 14:19 | comment | added | grjj3 | I already proposed one such construction: first, we need to rotate the system such that one of its axes (say $z$) points in the direction of $\hat{n}$. This can be achieved by taking $\alpha = \varphi$ (rotate the system around $z$ by the azimuthal angle of $\hat{n}$, such that $\hat{n}$ now lies in the $xz$ plane of the rotated system) and $\beta=\theta$ (rotate the new system through the polar angle of $\hat{n}$ about the previously rotated $y$ axis). Now, when $\hat{n}$ and $z$ coincide, rotate the system around $z$ by an amount of $\phi=2\pi$. But this construction seems to be wrong. | |
| Oct 6, 2020 at 13:56 | comment | added | grjj3 | @CosmasZachos - I updated my question and added the Wigner-D matrix calculation for $j=1/2$ and the proposed angles. Clearly, the proposed angles are wrong and I would like to understand why. | |
| Oct 6, 2020 at 13:54 | history | edited | grjj3 | CC BY-SA 4.0 |
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| Oct 6, 2020 at 13:39 | comment | added | grjj3 | @CosmasZachos - I understand the definition but I'm not sure about the exact relationship between the Euler angles and $\hat{n}$. The proposed angles $\alpha=\varphi,\beta=\theta,\gamma=\phi = 2\pi$ (which intuitively make sense) don't actually yield $D_{m'm}^{j}(\alpha ,\beta ,\gamma )=-\mathbb{I}_{2\times 2}$ as one would expect in the aforementioned example. Note that I work in the standard $zyz$ convention. | |
| Oct 6, 2020 at 13:33 | comment | added | Cosmas Zachos | Are you conflicted about the definition? You may compose the three Euler angles to an $\phi \hat n$. | |
| Oct 6, 2020 at 13:26 | history | edited | grjj3 | CC BY-SA 4.0 |
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| Oct 6, 2020 at 12:31 | history | asked | grjj3 | CC BY-SA 4.0 |