Timeline for Matrix elements $\langle n,k|x|n',k'\rangle$ for Bloch states
Current License: CC BY-SA 4.0
13 events
| when toggle format | what | by | license | comment | |
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| S Jul 14 at 10:07 | history | edited | Vincent Thacker | CC BY-SA 4.0 |
MathJax improvement
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| S Jul 14 at 10:07 | history | suggested | CompassBearer | CC BY-SA 4.0 |
MathJax improvement
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| Jul 14 at 9:01 | review | Suggested edits | |||
| S Jul 14 at 10:07 | |||||
| Jul 12, 2022 at 10:33 | vote | accept | dsfkgjn | ||
| Jun 8, 2022 at 7:07 | comment | added | schris38 | Okay. I have noticed some errors in my derivation. I have corrected them. The sign difference still remains though. I think it can be fixed by noting that my k derivative acts on $u^*$ instead of $u$ (which is where it acts on the paper!). However, $u$ does not depend on k, but it depends on $k'$. So it is possible that they mean derivative wrt $k'$ there. | |
| Jun 8, 2022 at 7:05 | history | edited | schris38 | CC BY-SA 4.0 |
added 9 characters in body
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| Jun 8, 2022 at 7:00 | comment | added | schris38 | And I also think that I have a mistake in the calculations. I will correct it now | |
| Jun 8, 2022 at 6:59 | comment | added | schris38 | Maybe this has something to do with the fact that the derivative wrt $k$ is equal to minus the derivative wrt $k'$ | |
| Jun 8, 2022 at 6:53 | comment | added | dsfkgjn | Of course - I am confused why the result from the paper does not have this sign difference. | |
| Jun 7, 2022 at 13:06 | comment | added | schris38 | If you mean the difference of signs between the first and the second terms, the latter (difference) exists due to integration by parts. I.e. $\partial_k[e^{i(k-k')x}f(k)]=\partial_k[e^{i(k-k')x}]f(k)+e^{i(k-k')x}\partial_k[f(k)]$. I am not sure what it is you ask for the positioning of the $\partial_k$ operator... It should act on a function of $k$, so I can not move it around in an arbitrary way... Please ask freely if there are more things you want to ask | |
| Jun 7, 2022 at 10:14 | comment | added | dsfkgjn | This got me nearly there. Small question: can you account for the difference in signs in the last line? And the positioning of the $\partial_k$ operator? | |
| Jun 7, 2022 at 10:05 | history | bounty ended | dsfkgjn | ||
| Jun 6, 2022 at 10:53 | history | answered | schris38 | CC BY-SA 4.0 |