Timeline for On addition of angular momenta and inner product
Current License: CC BY-SA 4.0
16 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 16, 2021 at 0:00 | history | tweeted | twitter.com/StackPhysics/status/1415823554256547864 | ||
| Jul 15, 2021 at 19:47 | history | became hot network question | |||
| Jul 15, 2021 at 15:37 | comment | added | ZeroTheHero | yes the commutator is $0$ since $J_{1x}$ and $J_{2x}$ etc act in different spaces. | |
| Jul 15, 2021 at 12:33 | vote | accept | ric.san | ||
| Jul 15, 2021 at 12:32 | answer | added | Tobias Fünke | timeline score: 4 | |
| Jul 15, 2021 at 12:23 | comment | added | Voulkos | See my F O U R T H___ A N S W E R here : Total spin of two spin- 1/2 particles. Especially all after equation (68). | |
| Jul 15, 2021 at 12:21 | comment | added | ric.san | I've added a comment in the related post @Jakob suggested: physics.stackexchange.com/questions/422369/… | |
| Jul 15, 2021 at 12:02 | comment | added | ric.san | Thanks, that was actually my second doubt. You've written $2 J_1 \cdot J_2$, so the commutator $[J_1, J_2]$ should be zero. But is it true? Even for two interacting systems? | |
| Jul 15, 2021 at 12:00 | comment | added | ZeroTheHero | Note that it does boil down to $J_1^2+J_2^2+2 J_1\cdot J_2$ where $J_1\cdot J_2=J_{1x}J_{2x}+J_{1y}J_{2y}+J_{1z}J_{2z}$ with $J_{1x}=J_x\otimes \mathbb{I}$ etc. | |
| Jul 15, 2021 at 11:56 | comment | added | Tobias Fünke | See for example this or this related post and the definition that @ZeroTheHero gave. I wanted to point out that you have made a mistake in the calculation, e.g. the first term of your last line is wrong (it must be an operator on the tensor Hilbert space, so $J_1^2 \otimes \mathbb{I}_2$). | |
| Jul 15, 2021 at 11:55 | comment | added | ric.san | @ZeroTheHero yes, I'd just see how to derive it from the definition of $J$. | |
| Jul 15, 2021 at 11:52 | comment | added | ric.san | @Jacob you've written the composition of two operators, not their inner product, I think. I'm wondering how to compute $(A \otimes B) \cdot (C \otimes D)$ | |
| Jul 15, 2021 at 11:51 | comment | added | ZeroTheHero | $J^2=J_x^2+J_y^2+J_z^2$ where $J_x=J_x\otimes \mathbb{I} + \mathbb{I}\otimes J_x$ etc in your notation. | |
| Jul 15, 2021 at 11:50 | comment | added | aneet kumar | Could you specify what is your doubt? | |
| Jul 15, 2021 at 11:49 | comment | added | Tobias Fünke | Note that $(A \otimes B) (C \otimes D) = (AC) \otimes (BD)$. Could you specify your question? 'What does it all mean?' is a very broad question. | |
| Jul 15, 2021 at 11:45 | history | asked | ric.san | CC BY-SA 4.0 |