Timeline for Mathematica Crashes with low memory warning Trying to solve Schroedinger Equation in a box with initial constraints
Current License: CC BY-SA 3.0
15 events
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| Apr 22, 2015 at 1:08 | vote | accept | catadoxas | ||
| Apr 21, 2015 at 22:19 | comment | added | catadoxas | my point is that there should only be 1 such normalization constant for all of t, but youre ofcourse right about linearity, I can just scale the result of your equation | |
| Apr 21, 2015 at 22:14 | comment | added | Jens | Normalization factors are irrelevant in a linear differential equation, so you can add any scaling you want after the calculation of $\psi$, instead of cluttering up the solution process with numerical constants. It's always best in numerics to reduce the number of parameters to the minimum relevant set. The consistent way of normalizing the result is to do an integral over the absolute square of the result at an arbitrary time over the box, and divide by the square root of that number. For plotting a movie with normalization, you additionally have to fix the color scale. | |
| Apr 21, 2015 at 22:06 | comment | added | catadoxas | basically there is a theorem that states, that if you can Normalize the wavefunction so that Integrate psi^2[x,y,0] dy dx == 1 then the wavefunction will stay normalized for all of t. So to use it for any sort of probabalistic analysis, I have to normalize the wavefunction | |
| Apr 21, 2015 at 22:03 | comment | added | catadoxas | What im now trying to plot is what you gave me, but with my old normalized wavefunction (normal curve instead of gaussian), I realize that I took a rather narrow function (its been calculating the better part of an hour), should this finish? my main problem with the distribution you use is, that I dont know how to normalize it (I think it shifts if it isnt centered on 0 and I scale it?) | |
| Apr 21, 2015 at 21:08 | history | tweeted | twitter.com/#!/StackMma/status/590623213547302912 | ||
| Apr 21, 2015 at 21:07 | comment | added | Jens |
Maybe I can add some more explanations later. The Array with slots # is a shorter way of constructing one of the lists I need. You could do the same with another Table construct. Array is just shorter sometimes, especially here since it doesn't require me to define an additional table index variable. The slots # and #2 are then the stand0ins for the table indices I didn't want to name.
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| Apr 21, 2015 at 20:49 | history | edited | catadoxas | CC BY-SA 3.0 |
added 204 characters in body
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| Apr 21, 2015 at 20:41 | history | edited | catadoxas | CC BY-SA 3.0 |
added 325 characters in body
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| Apr 21, 2015 at 17:39 | answer | added | Jens | timeline score: 7 | |
| Apr 21, 2015 at 15:38 | comment | added | catadoxas | I would not mind long computation times btw. If I can run it over night id be fine with it | |
| Apr 21, 2015 at 15:37 | comment | added | catadoxas | Oh I didnt mean to pretend I came up with all of this on my own, yes I also normalized the wavefunction so that psi^2 integrated = 1. thanks for pointing out the problem with pseudospectral method. Im not sure I understand you on your second point. this was ment to be more of a demo problem to calculate more difficult problems later on. so for general solutions to the 2-d particle in a box problem wouldnt I need the time dependant version? say for an arbitrary normalized psi[x,y,0]? | |
| Apr 21, 2015 at 15:08 | comment | added | Jens | A more efficient approach for this simple example would be to expand in eigenfunctions of the time-independent equation with Dirichlet conditions. | |
| Apr 21, 2015 at 15:07 | comment | added | Jens | What you did here is take the approach from this answer and made two changes: narrowed the initial wave packet, requiring a lot more spatial points for an accurate discretization, and changed the boundary conditions from periodic to Dirichlet, which is inconsistent with the pseudospectral method. | |
| Apr 21, 2015 at 14:28 | history | asked | catadoxas | CC BY-SA 3.0 |