Timeline for Yukawa potential in higher dimensions
Current License: CC BY-SA 4.0
16 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 23, 2020 at 13:06 | vote | accept | SaMaSo | ||
| Sep 22, 2020 at 12:18 | comment | added | Adam | @SaMaSo it is not a jump, it is a crossover from one powerlaw to the other as $r$ increases above $1/m$. For $m=0$, it never happens, and you just get Coulomb. | |
| Sep 22, 2020 at 11:10 | comment | added | SaMaSo | @Adam I just can't imagine how the exponent can suddenly jump from $(n-1)/2$ to $n-2$ when $m$ is lowered. Otherwise I understand the mathematical reasoning. | |
| Sep 22, 2020 at 10:53 | comment | added | Adam | @SaMaSo As explained by Artem Alexandrov, you do recover the Coulomb potential in the limit $m\to 0$. It is just that in the limit $r\gg 1/m$, you do not get $\exp(-mr)/r^{n-2}$ but $\exp(-mr)/r^{(n-1)/2}$, which is identical only for n=3! The reason, as can be deduced from Artem's answer, is that the limit $r\gg 1/m$ for $m=0$ is never reached for any finite $r$ (even very large), and the powerlaw behavior is thus modified. | |
| Sep 22, 2020 at 9:00 | history | tweeted | twitter.com/StackPhysics/status/1308330197444440064 | ||
| Sep 21, 2020 at 19:07 | answer | added | Artem Alexandrov | timeline score: 2 | |
| Sep 21, 2020 at 18:38 | comment | added | Artem Alexandrov | @SaMaSo you can obtain the desired asymptotic behavior in the limit of $r\gg 1/m$, which can be done with help of the steepest descent of the integral over $\alpha$ | |
| Sep 21, 2020 at 18:35 | comment | added | Artem Alexandrov | @SaMaSo can this help physics.stackexchange.com/questions/562908/… ? | |
| Sep 21, 2020 at 16:06 | comment | added | SaMaSo | @Adam shouldn't the limit of $m\to 0$ give the Coulomb potential? | |
| Sep 21, 2020 at 10:32 | history | edited | SaMaSo | CC BY-SA 4.0 |
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| Sep 21, 2020 at 10:30 | comment | added | Adam | Have you considered the fact that the argument made in the other post is not true? A back of the envelop stationary phase argument seems to show that you are correct, and that asymptotically, you have $\exp(-mr)/r^{(n-1)/2}$. | |
| Sep 21, 2020 at 10:26 | comment | added | Qmechanic♦ | General tip: Let's not have posts look like revision histories. | |
| Sep 21, 2020 at 9:33 | history | edited | SaMaSo | CC BY-SA 4.0 |
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| Sep 21, 2020 at 9:22 | history | edited | SaMaSo | CC BY-SA 4.0 |
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| Sep 21, 2020 at 8:56 | history | edited | SaMaSo | CC BY-SA 4.0 |
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| Sep 21, 2020 at 8:01 | history | asked | SaMaSo | CC BY-SA 4.0 |