Timeline for Solving a time-dependent Schrödinger equation
Current License: CC BY-SA 4.0
24 events
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| S Apr 5, 2022 at 12:39 | history | suggested | Glorfindel | CC BY-SA 4.0 |
broken link fixed
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| Apr 5, 2022 at 5:20 | review | Suggested edits | |||
| S Apr 5, 2022 at 12:39 | |||||
| May 13, 2016 at 3:52 | comment | added | xslittlegrass | Another common method is splitting operator method which can conserve the norm. | |
| Mar 27, 2013 at 16:23 | history | edited | acl | CC BY-SA 3.0 |
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| Mar 21, 2013 at 20:54 | comment | added | acl | @Zahra just click where it says "continue this discussion in chat" in my comment above | |
| Mar 21, 2013 at 20:54 | vote | accept | tenure track job seeker | ||
| Mar 21, 2013 at 20:54 | comment | added | tenure track job seeker | Sorry I was working on another code and I have just seen your comment. Yes sure, I just don't know how I can find you ... | |
| Mar 21, 2013 at 19:26 | comment | added | acl | @Zahra any chance of going to the chat room above? | |
| Mar 21, 2013 at 18:51 | comment | added | tenure track job seeker | Thanks A LOT for all your help. I am now trying to use it for my own problem. Your explanation helped me a lot. I appreciate that. | |
| Mar 21, 2013 at 18:50 | comment | added | acl | let us continue this discussion in chat | |
| Mar 21, 2013 at 18:13 | history | edited | acl | CC BY-SA 3.0 |
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| Mar 21, 2013 at 17:10 | comment | added | acl | @Zahra not a problem, ask away. Basically, it constructs the operator $U(0,\tau)$ mentioned earlier, by explicitly propagating the system over lots of small time intervals, over which the propagator is just the exponential of the instantaneous Hamiltonian times dt; so it just multiplies all these exponentials together (time-slicing). | |
| Mar 21, 2013 at 16:50 | comment | added | tenure track job seeker |
Thanks 1000 times for your answer. I think it is going to solve my problem. I will continue using this method. However, I have some questions regarding your code: Can you please explain what your are doing in the second part of your code? What is constructU? Sorry for taking a lot of your time ...
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| Mar 21, 2013 at 16:23 | history | edited | acl | CC BY-SA 3.0 |
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| Mar 21, 2013 at 16:21 | history | edited | rm -rf♦ | CC BY-SA 3.0 |
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| Mar 21, 2013 at 16:06 | history | edited | acl | CC BY-SA 3.0 |
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| Mar 21, 2013 at 16:04 | comment | added | acl |
here you go (I had actually done this the first time, just posted only the time-independent limit because I did not realize you had a time-dependent hamiltonian). Note that the way I construct the Manipulate is not efficient because I recalculate $U$ from scratch all the time, but it's fast enough...
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| Mar 21, 2013 at 16:01 | history | edited | acl | CC BY-SA 3.0 |
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| Mar 21, 2013 at 15:58 | comment | added | acl | @Zahra oh I see, no, what I suggest is fully numerical. You're absolutely right that such problems cannot be solved analytically in general. OK let me write it up quickly and you can see if it's useful (I routinely use this on systems with much bigger Hilbert spaces than yours, up to 20-30000) | |
| Mar 21, 2013 at 15:55 | comment | added | tenure track job seeker | Thanks a lot for the time that you give to ask my question. I really appreciate that. I'm not insisting to solve my problem with NDSolve. It would be great if I can solve it the way you are explaining. I just thought it is not possible to solve it non-numerically. Can you please tell me how to do that? I appreciate it. | |
| Mar 21, 2013 at 15:35 | comment | added | acl |
@Zahra For a time-dep H, you can simply construct the propagator from $t=0$ to some time $t=\tau$, say. I can explain how if you want. but let me know if you actually want so I don't waste my time if you insist on doing it with NDSolve--but ask yourself which is the most practical way if you have a hilbert space of dimension 20000, for instance (so you'd need to solve 20000 coupled ODEs with your approach)
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| Mar 21, 2013 at 13:49 | comment | added | tenure track job seeker | Thanks a lot for all this. However as you mentioned in your previous comment, my problem is a time-dependent schrodinger equation. In this case, the Hamiltonian doesn't commute in different times, and it can't just be a simple exponential; it should be a path ordered exponential. This is the reason that I can't do this. Such this problems don't have an analytical solution, they ave to be solved numerically!! | |
| Mar 21, 2013 at 13:46 | history | edited | acl | CC BY-SA 3.0 |
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| Mar 21, 2013 at 13:32 | history | answered | acl | CC BY-SA 3.0 |