Timeline for Identical Particles Combinatorial approach Wave function (anti)symmetrization
Current License: CC BY-SA 4.0
10 events
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| Feb 26, 2023 at 14:59 | comment | added | Cosmas Zachos | Yes. Are you familiar with Nakahara's book referenced here? As for your first question, I don't know how your source can bypass symmetry, as you claim: maybe you have to chase down its reference and review it here... | |
| Feb 26, 2023 at 11:22 | comment | added | curious_mind | @CosmasZachos I also have an additional question. Let's say the system is thermally excited and at equilibrium at some non zero finite temperature. I think it is possible to calculate possible ways combinatorically. Or still it is not ? | |
| Feb 26, 2023 at 4:09 | comment | added | curious_mind | @CosmasZachos answer 20 is given. But I do not think, it is given based on addition of 5 spin and CG technology. I mean, I am not sure I am lucky for this particular problem unless I find out 5 spin wavefunctions and count how much of them is antisymmetric. OR you mean for this problem it might not be required ? | |
| Feb 25, 2023 at 17:03 | comment | added | Cosmas Zachos | In your original question answer you already did take antisymmetrization into account! You realized there is only room for 2 fermions in the ground state, and you were lucky there was space for the other 3 in the first excited state, which is a constraint imposed by antisymmetry. I believe that you were just lucky the ground state does not block the first excited state fermions for the lowest total energy state, but you may not always be this lucky.... | |
| Feb 25, 2023 at 14:42 | history | edited | Qmechanic♦ | CC BY-SA 4.0 |
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| Feb 25, 2023 at 14:11 | comment | added | ZeroTheHero | It might work but is likely intractable for larger number of particles. Plus there are subtleties with repeated irreps which, unless you know how many irreps there are, will certainly defeat you. For two particles it’s easy enough but even with 3 you’d have to do quite a bit of work. | |
| Feb 25, 2023 at 13:44 | comment | added | curious_mind | So combinatorial approach as described above will not work ? Thanks for resource suggestion | |
| Feb 25, 2023 at 13:13 | comment | added | ZeroTheHero | You need Young diagram techniques for this. In particular, there will be repeated values of total $S$. Probably the best source is Ping J, Wang F, Chen JQ. Group representation theory for physicists. World Scientific Publishing but if you do not understand CG technology this might be a struggle. See this post for some details with $4$ particles. | |
| Feb 25, 2023 at 13:06 | history | edited | ZeroTheHero | CC BY-SA 4.0 |
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| Feb 25, 2023 at 7:57 | history | asked | curious_mind | CC BY-SA 4.0 |