Timeline for Understanding the virtual states referenced in multiphoton absorption studies
Current License: CC BY-SA 4.0
34 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 8, 2023 at 12:01 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Apr 7, 2023 at 7:04 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Nov 28, 2022 at 15:09 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Jul 30, 2022 at 13:01 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Mar 30, 2022 at 22:03 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Feb 20, 2022 at 9:56 | history | edited | Urb | CC BY-SA 4.0 |
deleted 62 characters in body
|
| Feb 20, 2022 at 4:05 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Oct 18, 2021 at 16:04 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Jun 20, 2021 at 15:03 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| May 14, 2021 at 15:52 | answer | added | Above Threshold | timeline score: 1 | |
| Dec 10, 2013 at 0:45 | history | edited | RGrey | CC BY-SA 3.0 |
added 448 characters in body
|
| Dec 10, 2013 at 0:41 | comment | added | RGrey | @WetSavannaAnimalakaRodVance This paper (arxiv.org/pdf/1209.5620.pdf) seems to do a decent job at explaining the interaction Hamiltonian for two-photon absorption (see Section 2). I'm reading through it now. | |
| Dec 9, 2013 at 23:21 | comment | added | Selene Routley | I also found (if you haven't already) the review article by Roberts "Rigged Hilbert Space in Quantum Mechanics" here | |
| Dec 9, 2013 at 22:53 | comment | added | Selene Routley | ...example exclusively in mind - for QM you won't need anything else. So the set of bras is strictly bigger than the set of kets, so I'm guessing that the virtual states probably find an interpretation in $S^*\sim S$. So Todd Trimble is exactly right in his suspicions that the usual triple is $S\subset \mathbf{L}^2(\mathbb{R}^N)\subset S^*$ with $S$, $S^*$ the Scwhartz space and tempered distributions. | |
| Dec 9, 2013 at 22:51 | comment | added | Selene Routley | ...distributions in $S^*$ (by "ferret out" I'm saying that the topology is strong enough to make things like the Dirac delta into a continuous functional, whereas it isn't continuous with respect to the Hilbert space norm). There's a great deal of detail that's glossed over and I'd suggest you should take a specific example $S$ = Schwartz space and $S^*$ = Tempered Distributions and keep this relatively simple (and, for QM most relevant) .... | |
| Dec 9, 2013 at 22:50 | comment | added | RGrey | @WetSavannaAnimalakaRodVance That MathOverflow link looks to be quite helpful... | |
| Dec 9, 2013 at 22:46 | comment | added | Selene Routley | Yes, the Hamiltonian with terms like this will give a good working model, but one has no idea what co-efficients $\kappa(\nu_1,j_1,\nu_2,j_2)$ to put it: these would hopefully come out of a fuller analysis. In the meanwhile, if you're struggling with rigged Hilbert space, you might see physics.stackexchange.com/a/43519/26076 and also the discussions mathoverflow.net/q/43313. The Wikipedia page is a bit light on: it glosses over the fact that the "smooth" functions $S$ have to be kitted with a stronger topology than in the Hilbert space so that the topology can "ferret out" ... | |
| Dec 9, 2013 at 22:42 | history | edited | RGrey | CC BY-SA 3.0 |
edited body
|
| Dec 9, 2013 at 22:27 | history | edited | RGrey | CC BY-SA 3.0 |
added 348 characters in body
|
| Dec 9, 2013 at 22:14 | comment | added | RGrey | @WetSavannaAnimalakaRodVance I look forward to seeing what you can come up with! I've been reading about the electric dipole approximation, and I did think of using a coupling Hamiltonian to describe the virtual state, but it's unclear to me how to proceed in a rigorous way w.r.t. the virtual state. | |
| Dec 9, 2013 at 10:32 | history | tweeted | twitter.com/#!/StackPhysics/status/409993961303191552 | ||
| Dec 8, 2013 at 22:16 | comment | added | Selene Routley | ... in the coupling of the molecule with the EM field and these are the lines I'll try thinking along. | |
| Dec 8, 2013 at 22:14 | comment | added | Selene Routley | Fantastic! The original is enough! I shall have a look through the papers you cite: your question is an excellent one and I shall think about it some more. A trite answer is that the "memory" can be in a phenomenological model: we could add terms to the Hamiltonian of the form $\kappa(\nu_1,j_1,\nu_2,j_2)\, a_0^\dagger \,a(\nu_1,j_1)\, a(\nu_2,j_2) + H.c.$ where $a_0^\dagger$ raises the molecule state and $a(\nu,j)$ the annihilation operator for EM mode $j$ at frequency $\nu$ but I suspect this doesn't help much. You've likely already thought of the obvious that the "memory" could be .... | |
| Dec 8, 2013 at 19:55 | comment | added | RGrey | @WetSavannaAnimalakaRodVance Thanks for your comment. I updated my question with two papers by Gadella, M. that I was looking at - I've had trouble finding other relevant papers. Also, here's Goppert-Mayer's original paper (onlinelibrary.wiley.com/doi/10.1002/andp.19314010303/pdf) for free, but I don't have a translation. | |
| Dec 8, 2013 at 19:49 | history | edited | RGrey | CC BY-SA 3.0 |
added 526 characters in body
|
| Dec 7, 2013 at 9:02 | comment | added | Selene Routley | Can you give a reference for some of the papers you speak of (especially the rigged Hilbert space)? Do you have Göppert‐Mayer's original paper? "Über Elementarakte mit zwei Quantensprüngen", Annalen der Physik vol 401 issue 3 1931? There is a translation also, both behind paywalls. | |
| Dec 7, 2013 at 5:15 | history | edited | RGrey | CC BY-SA 3.0 |
added 103 characters in body
|
| Dec 7, 2013 at 5:02 | history | edited | RGrey | CC BY-SA 3.0 |
added 191 characters in body
|
| Dec 6, 2013 at 0:13 | history | edited | RGrey | CC BY-SA 3.0 |
edited title
|
| Dec 5, 2013 at 23:27 | history | edited | Brandon Enright |
edited tags
|
|
| Dec 5, 2013 at 23:17 | history | edited | RGrey | CC BY-SA 3.0 |
added 257 characters in body
|
| Dec 5, 2013 at 20:02 | history | edited | RGrey | CC BY-SA 3.0 |
added 26 characters in body
|
| Dec 5, 2013 at 19:10 | review | First posts | |||
| Dec 5, 2013 at 19:20 | |||||
| Dec 5, 2013 at 18:52 | history | asked | RGrey | CC BY-SA 3.0 |