Timeline for Schroedinger operator in 2 dimensions with singular potential
Current License: CC BY-SA 4.0
11 events
| when toggle format | what | by | license | comment | |
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| Feb 26 at 18:30 | history | edited | Christian Remling | CC BY-SA 4.0 |
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| Feb 26 at 17:50 | history | rollback | Christian Remling |
Rollback to Revision 3
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| Feb 26 at 17:45 | history | edited | Christian Remling | CC BY-SA 4.0 |
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| Feb 26 at 10:58 | vote | accept | António Borges Santos | ||
| Feb 26 at 4:22 | history | edited | Christian Remling | CC BY-SA 4.0 |
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| Feb 25 at 21:50 | comment | added | António Borges Santos | ah, but you think the domains will be different for $c \neq 0$ from the ones you can obtain for $c=0.$ So both (1) and (2) are wrong. | |
| Feb 25 at 21:49 | comment | added | Christian Remling | @AntónioBorgesSantos: No, I'm just saying that we can decompose $-\Delta=\bigoplus H_n$ and then extend this, and since the $H_n$, $n\not= 0$ are already essentially self-adjoint, it's only about finding a domain for $H_0$. This works for any $c\in\mathbb R$, including $c=0$. | |
| Feb 25 at 21:45 | comment | added | António Borges Santos | Thanks Christian, I think I still stumble over the same point: You say "we can just set 𝑐=0 in this analysis and everything is still correct". Are you suggesting that the conditions are in some sense independent of setting $c=0$ as long as $c<1$? This is not obvious to me. | |
| Feb 25 at 21:34 | history | edited | Christian Remling | CC BY-SA 4.0 |
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| Feb 25 at 21:12 | comment | added | António Borges Santos | So you are saying the Dirichlet domain is indeed an admissible domain? If I read your answer correctly, then you are saying that we just have to know the self-adjoint extensions of the Laplacian and we will have a complete description for $c<1$? | |
| Feb 25 at 21:09 | history | answered | Christian Remling | CC BY-SA 4.0 |