Timeline for Time evolution of a wave packet from the time-independent Schroedinger equation [duplicate]
Current License: CC BY-SA 3.0
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| Apr 13, 2017 at 12:55 | history | edited | CommunityBot |
replaced http://mathematica.stackexchange.com/ with https://mathematica.stackexchange.com/
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| Apr 17, 2015 at 20:03 | history | closed |
Jens bbgodfrey Öskå m_goldberg ciao |
Duplicate of Complex valued 2+1D PDE Schrödinger equation, numerical method for `NDSolve`? | |
| Apr 17, 2015 at 18:10 | history | edited | m_goldberg | CC BY-SA 3.0 |
Routine clean-up
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| Apr 17, 2015 at 16:24 | review | Close votes | |||
| Apr 17, 2015 at 20:03 | |||||
| Apr 16, 2015 at 17:20 | comment | added | Jens | If the link in my previous comment answers your question, then I think the question can be closed. The second part is Taylor's formula: $\exp(a \partial/\partial x) f(x) = f(x+a)$. | |
| Apr 16, 2015 at 17:01 | comment | added | Jens | For the second part of the question, I assume you want a more general operator $\exp(\alpha \partial/\partial \theta)$, because without the additional parameter $a$ the expression would be pretty useless. One could see that part as a duplicate of Exponential of a Differential Operator. But if you could be more specific about the actual problem and your solution attempts, there may be a way to give a more specific answer, too. | |
| Apr 16, 2015 at 16:46 | history | edited | SquareRoot2 | CC BY-SA 3.0 |
added 6 characters in body
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| Apr 16, 2015 at 16:42 | answer | added | 2012rcampion | timeline score: 1 | |
| Apr 16, 2015 at 16:42 | comment | added | Jens |
So then you want something like this, right? Complex valued 2+1D PDE Schroedinger equation, numerical method for NDSolve?
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| Apr 16, 2015 at 16:40 | comment | added | SquareRoot2 | @Jens, Starting with a solution of the time-independent problem, one can propagate it in time using $\exp (- \mathrm{i} H t / \hbar)$ to obtain $\psi(t)$, so the problems are related. If you want, equivalently, you can find $\psi (t)$ directly from the time-dependent equation and compute $\langle \theta \rangle$. Note: I'm not trying to solve the TISE, I'm just trying to evolve a given wave packet which is NOT necessarily a solution of the TISE (read as eigenstate of $H$). | |
| Apr 16, 2015 at 16:35 | comment | added | 2012rcampion | Shouldn't it be $\exp(\partial_x)\left\{x^2\right\} = 1 + 2x + x^2$? | |
| Apr 16, 2015 at 16:35 | comment | added | Jens | This is a time-independent problem, and your first link is to a time-dependent solution. They are very different problems. Also the link doesn't use the time-ordering operator (although it's mentioned), it just discretizes time. If you want to a time-dependent 2D problem, see this link. | |
| Apr 16, 2015 at 16:23 | history | edited | SquareRoot2 | CC BY-SA 3.0 |
Clarified question about dangling exponential.
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| Apr 16, 2015 at 15:58 | comment | added | user9660 | Welcome to Mathematica.SE! I suggest the following: 1) As you receive help, try to give it too, by answering questions in your area of expertise. 2) Read the faq! 3) When you see good questions and answers, vote them up by clicking the gray triangles, because the credibility of the system is based on the reputation gained by users sharing their knowledge. Also, please remember to accept the answer, if any, that solves your problem, by clicking the checkmark sign! | |
| Apr 16, 2015 at 15:44 | review | First posts | |||
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| Apr 16, 2015 at 15:40 | history | asked | SquareRoot2 | CC BY-SA 3.0 |