# Should we allow questions asking the mathematical solution to physics problems?

An example question:
Solution for the Finite 2D Potential Well - Rotational Symmetry

It is being voted to close as off-topic. Reading the comments, that seems to be because it the physics is basically done, all that's left is to solve a differential equation. That is true, but I wonder if it's really a problem.

That question was just an example, let's focus on the general case. A lot of physics problems and exercises have very little physics and quite a lot of mathematics. Let us assume a question is asked where the physics is basically done, so that it is solvable through strictly mathematical procedures. The motivation is something like: the Lagrangian of a several body system, the velocity field of a fluid around a specific object, or the eigenstates of a QM system. Also assume the level is not too basic, so it is within our pre-established level.

Should we consider such a question off-topic?

Even though the answer only requires mathematics, it looks like the kind of question a physics student might be interested in. Do we want to keep it here or move it to math.stackexchange?

• I think we should keep that kind of questions since obviously they are relevant to physicists. – Robert Smith Jan 11 '11 at 20:15

Edit: In case it seems like I am answering a different question: I am not. I am just saying that it's not always clear what it means "that physics is basically done". This is because there are various ways physics can be done to reduce the problem to mathematical form and some of them are pretty bad resulting in horribly complex math problems that are completely unnecessary.

OTOH if by "physics is basically done" you meant that it was done in the right way and math is the only thing that remains to solve it then such problems are not welcome in my opinion.

At first I'd be tempted to move such questions over to the math sites (and I've voted to close some of those question myself in the past). But thinking more about it, sometimes physicists can give insight that mathematicians wouldn't provide.

What do I mean? Few (perhaps contrived) examples:

1. Trying to do computation in wrong coordinates (which don't make use of some symmetry, say). The calculation could still be carried out but will be tedious. Physicist will immediately set the OP straight by telling him "think again about choosing the $z$ axis you moron" (perhaps without the moron part).

2. Trying to solve equations in Newtonian formalism. Again, doable in principle. But physicist will point out that, passing to Lagrangian formalism, there are two conserved quantities and there is actually nothing to solve anymore.

3. Computing the tear of the space-time fabric. Brian Greene would recommend passing to the mirror dual Calabi-Yau (okay, I am just reading The Elegant Universe :-D).

What I am getting at is that are physical insights into purely mathematical problems. So we should move the questions only if its clear that they are too simple already. If the correct coordinates and formalism have been chosen already and all the symmetries and dualities exploited and there is nothing else left than tedious calculation then okay, let's move it over to math sites.

• +1 great points. – David Z Jan 12 '11 at 20:06
• I absolutely agree with David here :) – Robert Filter Jan 13 '11 at 21:39

At least some of the time, the physics isn't done just because you've reduced the problem to math (even if you've done the best possible reduction to math)...

...because, after you've cranked through the math you have to interpret the results.

To be sure for the typical introductory mechanics question the interpretation is trivial, but for real physics that is rarely the case.

In any case, I don't think that "reduced to math" is a good metric. What we are looking for is "there is still physics to do", and this may require some intelligence to suss out.

I don't like questions of this type, not because they are lacking in physics, but because they are such standard textbook problems. I'm sure I could find a couple of QM texts with this precise problem in the exercises. If we encourage questions like this it seems likely to me that we will start having people posting problems from their homework sets here and hoping to get answers and I think we should discourage that. Of course I am not saying that was the intention of the person who posted this question. It also reflects my opinion (which I'm sure not everyone agrees with) that it would be a good thing if this site had more emphasis on research level questions in physics.

• In my opinion homework questions are fine as long as OP includes a good reason why he wants us to help him. E.g. his/her failure of solving it (but not for a lack of trying!) or he/she wants to gain deeper understanding or maybe he/she had already solved it but is looking for a better solution. But I do agree that I'd also like the site to move more into the research direction and I wouldn't miss homework questions at all. – Marek Jan 13 '11 at 17:08
• I can see your point and can understand it very well. You might want to have a look at area51.stackexchange.com/proposals/23848/theoretical-physics . Greets – Robert Filter Jan 13 '11 at 21:52
• @Robert: Thanks, I hope that site gets going, but it seems to be taking a long time to get off the ground. – pho Jan 13 '11 at 23:23
• actually, it is doing pretty well in my opinion; usual area51 site takes about half a year to reach beta (if it reaches it at all). It's very hard to gain momentum at the beginning. I think physics.SE might help TP.SE get some attention now, as it is becoming a real thing, being mentioned on few famous blogs (okay, I know just about two, but they are as famous as they come). – Marek Jan 15 '11 at 21:19
• I would also say that textbook questions shouldn't be banned. This is simply based on my own experience. For exam preperation I did a lot of anlysis stuff and had questions regarding some tasks. I always asked on math.stackoverflow and got brilliant answers, which really took my understanding of the topic to the next level. It is very different reading a book compared to discussing my own approach of the problem. Of course I had tried to solve them on my own before, this is indeed a prerequesite. – ftiaronsem Jan 15 '11 at 23:46

Dear Bruce,

as the one putting up the question you mentioned I am willing to say something about it.

I am sure it might be trivial and also sure that most people here (well, I might include myself here) can write down the solution instantaneously.