Timeline for Is $n+\frac {1}{2}$ in Kendall-Mann numbers and quantum harmonic oscillator related?
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16 events
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| Jul 29, 2022 at 4:47 | comment | added | Tom Copeland | I read your comment at my blog post, Sorry, I can't add any info to that already provided by others here. There are a lot of connections among the Hermite and Laguerre families of polynomials associated with the quantum harmonic oscillator and a variety of combinatorial constructs so that it's plausible there is a connection. | |
| Jan 7, 2021 at 8:56 | comment | added | Anixx | Following the link you can see the formulas for quantum harmonic oscillator before and after | |
| Jan 6, 2021 at 17:31 | comment | added | Mikhail Gaichenkov | @Anixx How your approach would simplify the case and what would be the advantage? | |
| Jan 2, 2021 at 16:30 | comment | added | Anixx | physicsforums.com/threads/algebra-of-divergent-integrals.989043 | |
| Oct 21, 2019 at 12:50 | comment | added | Mikhail Gaichenkov | @Anixx Thank you. Could you clarify it a little more, any refernece on the regularization please? | |
| Oct 15, 2019 at 21:35 | comment | added | Anixx | 1/2 in quantum harmonic oscillator comes from the regularization of series $\sum_{k=0}^\infty 1 $ | |
| Apr 13, 2017 at 12:57 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
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| Apr 28, 2016 at 12:25 | comment | added | Mikhail Gaichenkov | @CarloBeenakker Well, by the way I am trying to see where Kendall-Mann numbers’ property and its Gaussian with known error of approximation (MO 164849) could be used. I heard that there is electron diffusion for high energized levels ( probably multiphoton processes in atoms). Can you guess something to apply the property and/or the distribution ( Gaussian for for the finite number N of mixing particles) to physics & an experiment? | |
| Apr 28, 2016 at 10:49 | comment | added | Carlo Beenakker | no relationship whatsoever, also notice that the 1/2 offset is not at all special for the harmonic oscillator, any bounded motion with two smooth turning points will give you the same offset. | |
| Apr 28, 2016 at 9:46 | comment | added | Mikhail Gaichenkov | @CarloBeenakker Thank you, Does that 'Kendall-Mann numbers do not appear' mean no relation based on math? I try to think about 1/2 in a way which could explain it & "zero-point motion" via the permuatationa & inversions of some mixing particles. Could you have a look at Ben Naim article 'On the Mixing of Diffusing Particles' reffered via the link please? mathoverflow.net/questions/164849/… | |
| Apr 27, 2016 at 16:24 | comment | added | Carlo Beenakker | the answer to your last question (whence the 1/2?) has a simple answer in terms of "zero-point motion", "Maslov index", "WKB turning points" --- I can elaborate, but the Kendall-Mann numbers do not appear. | |
| S Apr 27, 2016 at 15:09 | history | suggested | 1089 | CC BY-SA 3.0 |
$\frac {1}{2}$ instead of $1/2$ and other formatting fixes.
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| Apr 27, 2016 at 15:00 | review | Suggested edits | |||
| S Apr 27, 2016 at 15:09 | |||||
| S Apr 27, 2016 at 14:46 | history | suggested | Amir Sagiv | CC BY-SA 3.0 |
tags, latex and english
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| Apr 27, 2016 at 14:42 | review | Suggested edits | |||
| S Apr 27, 2016 at 14:46 | |||||
| Apr 27, 2016 at 14:38 | history | asked | Mikhail Gaichenkov | CC BY-SA 3.0 |