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Sep
20
comment Applying rules with functions to expressions with derivatives
I can't think of any general way of answering the "gotcha" question, but in the context of your question, there is no gotcha since my approach produces the output you want for each of the examples you gave, using rules as stated in the question title.
Sep
19
comment Applying rules with functions to expressions with derivatives
I'm not sure I understand what you're asking. This post is about "applying rules", isn't it? When you say you "don't really need pattern matching", how is that related to the question? What do you mean by "more canonical"?
Sep
15
comment Define operator algebra
Related: Having the derivative be an operator
Sep
14
comment Find eigen energies of time-independent Schrödinger equation
It should be possible to modify the function spectrum so that it would allow you to input the potential using matrix notation such as MatrixPower[x] and MatrixExp[x]. Then you can also treat your exact shape, which simplifies to MatrixExp expressions. I'll see if I can do that tomorrow... but the technique has its limitations, and different basis functions may work better. As another alternative for bound state problems, you could also spatially discretize the equation.
Sep
14
comment Find eigen energies of time-independent Schrödinger equation
That potential is very different from the example in your question: it has a bound and a continuous part of the spectrum. You can't hope to use this method for the positive-energy (unbounded) states of your potential. But it should work fine at energies sufficiently far away from the "ionization threshold". The same distinction between the two parts of your spectrum has to be made with any other method, too.
Sep
13
comment Method -> {“AxesInFront” -> False} for Graphics3D
Related: Arrows on axes in Plot3D
Sep
10
comment What is the difference between Reduce and Solve?
Another difference is mentioned in Inequalities with assumptions and constraints: Reduce doesn't use Assumptions.
Sep
7
comment ArcTan and Compile
@chyanog Thanks - I didn't know that. How did you test this?
Sep
6
comment Complex surface: Finding the perimeter of the union of multiple disc intersections
It's quite possible that the question is badly formulated and that your answer is what was intended. So +1.
Sep
6
comment Complex surface: Finding the perimeter of the union of multiple disc intersections
Then the end result is the intersection of $N$ circles, right? So there is no further need to form a union in the end. Then the final situation is actually easier to solve than the intermediate steps, especially if you're allowed to pick, e.g., three arbitrary circles out of the $N$ given circles. In the end, one has a shape with an $N$ fold rotation symmetry, but that can't be exploited for the intermediate steps. It would help a great deal if you showed what attempts at a solution you have already tried, and maybe to sketch the desired end product (maybe I misunderstood it).
Sep
6
comment ArcTan and Compile
@AndreasLauschke It's OK to leave the links for completeness, I'd say.
Sep
6
comment ArcTan and Compile
@AndreasLauschke I'm guessing you want to confirm the equivalence of the Arg and ArcTan methods. But the links don't seem to address the discrepancy between the definitions at the origin.
Sep
6
comment ArcTan and Compile
@AndreasLauschke Could you explain what the links above are intended for?
Sep
6
comment Guidelines on giving readable names to variables
For readable variable names, my own preference is to follow what Mathematica itself does for practically all function names that are composed of several words: use en.wikipedia.org/wiki/Camelcase, except for the first letter of the variable which should be lower case to distinguish it from built-in names (which are always capitalized).
Sep
5
comment Blank VectorPlot
@Blackbird You're not plotting the desired function at all if you replace x and y by constants.
Sep
5
comment Blank VectorPlot
@Blackbird I've tried my solution in version 8 and 9, and it does the trick. In both cases, the Abs'[...] was the culprit. Not sure what exactly you did.
Sep
4
comment Writing intelligent replacement rules for symbols
This is part of the answer. However, the rules also require non-commuting operations, so even the starting point using Power or Times here isn't actually correct for the desired application.
Sep
4
comment Writing intelligent replacement rules for symbols
Have a look at this question
Sep
4
comment How to make traditional output for derivatives
Maybe this blog entry which is linked in the earlier answers I linked to will answer this. Defer is discussed as an alternative there, too.
Sep
1
comment How to find the domain and range of an implicit function?
All your examples are polynomial equations.