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Apr
18
comment Analogue for Maple's dchange - change of variables in differential expressions
I don't know much about Maple, but it seems from your examples that it's less "careful" when simplifying expressions: Mathematica leaves expressions unevaluated if it can't get a result that's valid generically or consistent with the given assumptions. So probably one would have to allow an additional Assumptions option in the dChange emulation to tell Mathematica which variables are positive, or complex, etc... so it has a better chance of inverting and simplifying the required relations. Anyway, I like the idea...
Apr
18
comment compute the gradient in high dimension
@novice Thanks for the correction, I edited the answer to also include the comment by MichaelE2.
Apr
18
comment compute the gradient in high dimension
@MichaelE2 Oh sorry - I din't notice that. I'll double check and make the change. Thanks for pointing it out!
Apr
17
comment Solving differential equation
It seems that someone downvoted this answer. Is there any reason why one of my two approaches would be bad?
Apr
17
comment Eigen energies of 2D time independent Schrödinger equation
By imposing fixed values of the function on a square you're forcing an unphysical solution to this rotationally symmetric problem. It will probably violate the decaying boundary condition at infinity. So the setup of the problem in this 2D calculation is most likely incorrect, but definitely inconsistent with any kind of solution in polar coordinates that you mention as a comparison case.
Apr
16
comment Time evolution of a wave packet from the time-independent Schroedinger equation
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
comment Time evolution of a wave packet from the time-independent Schroedinger equation
It does seem like your answer belongs to that linked question, since this one mentions the exponential only as a part of the problem... but actually, the answer for the special case here is trivial: your operator, applied to any function $f(x)$, is simply equivalent to $f(x+1)$ by the Taylor formula.
Apr
16
comment Time evolution of a wave packet from the time-independent Schroedinger equation
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
comment Time evolution of a wave packet from the time-independent Schroedinger equation
(+1), but I think this part is a duplicate of Exponential of a Differential Operator
Apr
16
comment Time evolution of a wave packet from the time-independent Schroedinger equation
So then you want something like this, right? Complex valued 2+1D PDE Schroedinger equation, numerical method for NDSolve?
Apr
16
comment Time evolution of a wave packet from the time-independent Schroedinger equation
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
comment Make continuous 3D tube out of 2D image (Mathematica 8)
Although you're asking for a solution in an older version, the topic is already covered elsewhere: How to extrude a 3D image from a binary 2D image. Answers that apply to version 8 can also be found there.
Apr
15
comment Why is the Spherical Bessel Function acting strangely at this point?
Maybe it's worth pointing to the documentation of SetPrecision. (+1).
Apr
14
comment Trying to model Heat flow trough different materials with NDsolve
@xzczd A new question then sounds like a better idea.
Apr
14
comment ArcTan[x,y] problems
What do you mean by "continuous in (0,2 π)"?
Apr
14
comment Input of ions and compounds in Wolfram's Mathematica
To add this functionality to Mathematica proper is probably not possible in the framework of a StackExchange answer.
Apr
14
comment Rule transformations for compositions of tensor products
What have you tried so far?
Apr
13
comment Solving Lagrangian (4 vars to solve for)
I get no solution at all from your code. Make sure you clear all variables, maybe quit and restart.
Apr
13
comment sparse array with list
You can use the answer to the following question, of which this is a possible duplicate: Entering block matrices, general case doesn't work
Apr
12
comment Filling Piecewise Function leaves gaps
Try adding the option Exclusions -> None.