Timeline for Boundary Condition for Schrödinger Equation in Infinite Range
Current License: CC BY-SA 3.0
15 events
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| Feb 19, 2018 at 14:12 | history | edited | xzczd♦ | CC BY-SA 3.0 |
typo fixed.
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| May 13, 2017 at 3:58 | comment | added | xzczd♦ | @ivbc Yeah, it's undocumented, but it has been explained and used in this site for several times: mathematica.stackexchange.com/… . I've added some explanation to my answer. If you still have trouble in understanding it, feel free to ask. | |
| May 13, 2017 at 3:58 | history | edited | xzczd♦ | CC BY-SA 3.0 |
added 295 characters in body
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| May 12, 2017 at 19:33 | comment | added | ivbc | @xzczd, is it just me or is "Simplify`PWToUnitStep" an undocumented function??? Cant find it! | |
| May 11, 2017 at 3:38 | history | edited | xzczd♦ | CC BY-SA 3.0 |
small mistake in the explanation corrected.
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| May 11, 2017 at 3:24 | history | edited | xzczd♦ | CC BY-SA 3.0 |
add a simpler method for deducing neweq
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| May 11, 2017 at 3:10 | comment | added | xzczd♦ |
@ivbc Actually this is a function I place in SystemOpen@"init.m" file, because I adjust these options frequently when using NDSolve. (See Method -> mol[25, 4]? It's the same as writing Method -> {"MethodOfLines", "SpatialDiscretization" -> {"TensorProductGrid", "MaxPoints" -> 25, "MinPoints" -> 25, "DifferenceOrder" -> 4}}. ) I adjust these options because, as mentioned above, if I don't manually set "MinPoints" and "MaxPoints", NDSolveValue will choose a too large one because the initial condition is not smooth. (You can take away the option and see what will happen. )
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| May 10, 2017 at 20:36 | comment | added | ivbc | Wow, lots to learn from this answer! @xzczd, could you comment on the "mol" function? What does it do? Why did you use it? | |
| May 10, 2017 at 20:33 | vote | accept | ivbc | ||
| May 10, 2017 at 8:10 | comment | added | xzczd♦ | @zhk This transform makes the equation more complicated, of course :) , but by solving this equation instead, we obtain a better approximation for infinite range. (OP wants to solve the equation in $-\infty<x<\infty$. ) | |
| May 10, 2017 at 8:04 | comment | added | zhk | Does this simplify the problem? In what way this transformation helps? | |
| May 10, 2017 at 8:03 | comment | added | xzczd♦ |
@zhk Nope, in this transformation, only x is transformed to ξ. θ is a parameter. You can have a look at the linked post for more information.
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| May 10, 2017 at 7:49 | comment | added | zhk |
(+1) You have transformed x and tto xi and theta, right?
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| May 10, 2017 at 5:53 | history | edited | xzczd♦ | CC BY-SA 3.0 |
simplify the code a bit
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| May 10, 2017 at 4:32 | history | answered | xzczd♦ | CC BY-SA 3.0 |