Timeline for Jensen Polynomials for the Riemann Zeta Function
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 18, 2019 at 3:46 | comment | added | Michael Griffin | @Rudi_Birnbaum I had no idea about the connections to QM. Fascinating! | |
| Aug 5, 2019 at 7:25 | comment | added | Raphael J.F. Berger | In case you are interested on a bit more on these connections, I could explain it in more detail (somewhere more suitable). | |
| Aug 5, 2019 at 7:22 | comment | added | Raphael J.F. Berger | Now another nice thing is that all QM problems can be formulated in an style using differential equations or matrices. The Heisenberg uncertainty principle very naturally leads to "random matrices" in the matrix formulation. Now the particular problem of the harmonic oscillator (that leads to $H_n(X)$) is very specific in that is basically has $\Bbb N$ as energy eigenvalues themselves (not just some (unique)functions of $\Bbb N$) and moreover that the operation which usually introduces that famous "randomness" essentially leaves the algebraic form of the "solutions" ($H_n$) unchanged. | |
| Aug 5, 2019 at 7:16 | comment | added | Raphael J.F. Berger | This is very interesting work. I wanted to ask you @Michael Griffin, if you are aware of the role of $H_n(X)$ in Quantum Mechanics (QM)? Multiplied by $\exp(-\alpha X^2)$ for some positive $\alpha$ they represent the wave functions of the harmonic oscillator. Their zeros are called nodal "planes" (since often in QM $X\in\Bbb R^3$, but $\Bbb R$ is in this case equally important).Its one important general notion in quantum mechanics that the number of nodal planes almost always serves as a index for the central quantity "the energy"(an inherently real quantity)of the system under consideration. | |
| Feb 28, 2019 at 13:42 | vote | accept | Stopple | ||
| Feb 24, 2019 at 16:34 | comment | added | Stopple | See edit to the question | |
| Feb 23, 2019 at 3:45 | history | edited | Michael Griffin | CC BY-SA 4.0 |
added 17 characters in body
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| Feb 23, 2019 at 0:20 | history | answered | Michael Griffin | CC BY-SA 4.0 |