Timeline for Can indistinguishable particle wavefunctions be written as a product of total observable eigenstates?
Current License: CC BY-SA 4.0
14 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| S Oct 8, 2020 at 19:03 | history | bounty ended | CommunityBot | ||
| S Oct 8, 2020 at 19:03 | history | notice removed | CommunityBot | ||
| Sep 30, 2020 at 21:06 | answer | added | Something Different | timeline score: -2 | |
| Sep 30, 2020 at 19:01 | answer | added | ACuriousMind♦ | timeline score: 0 | |
| Sep 30, 2020 at 18:52 | comment | added | user2224350 | So, there are antisymmetric states for the three particle system, but still you cannot write them in the $\Psi_{total}$ form. Does this mean we need to introduce another quantum number? Probably not... | |
| Sep 30, 2020 at 18:50 | comment | added | user2224350 | Okay, but that's a different statement. Since all $\Psi_{total}$ of the above form (without the symmetry constraint tho) constitute a basis of the entire Hilbert space, they can obviously also be used to create a basis of the antisymmetric Hilbert space. But there is no single "product state" (space*spin) that could describe an antisymmetric state. | |
| Sep 30, 2020 at 18:30 | comment | added | ACuriousMind♦ | It is not obvious to me that the state you described cannot be written as the sum of basic tensors like $\Psi_\text{total}$, though. Again, please write it down explicitly - I find that the somewhat vague description in words doesn't make for good understanding what your problem is here. | |
| Sep 30, 2020 at 18:24 | comment | added | user2224350 | Consider my example above for 3 particles. You can still find antisymmetric states (eg put two particles with opposite spin in the a orbital and then the remaining one in the b orbital). But it's not possible to factor out the wavefunction in a spatial and a spin function | |
| Sep 30, 2020 at 18:22 | comment | added | ACuriousMind♦ | What state do you think is not expressible as a sum of states of that form? Please write it down explicitly. | |
| Sep 30, 2020 at 18:20 | comment | added | user2224350 | Well but the $\Psi_{total}$ don't neccesarily constitute a basis of the antisymmetric Hilbert space no? | |
| Sep 30, 2020 at 18:16 | comment | added | ACuriousMind♦ | Are you sure the people who say this aren't just being a bit sloppy with their language and what they mean is that a basis for the wavefunctions is given by $\Psi_\text{total}$ of that form? What part of the Hilbert space exactly do you think one "obviously" misses here? | |
| S Sep 30, 2020 at 17:59 | history | bounty started | user2224350 | ||
| S Sep 30, 2020 at 17:59 | history | notice added | user2224350 | Draw attention | |
| Sep 24, 2020 at 19:52 | history | asked | user2224350 | CC BY-SA 4.0 |