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For a long time the way I tended to see the Schrödinger equation written, some of the notation was like a foreign language to me, and so I couldn't work out how to actually use it to model anything, but then I saw it all the terms that were written out in what was a mathematical foreign language I didn't understand translated into a language I did, which allowed me to then work out how to use it to approximate the motion of particles through numerical methods.

Seeing as how I got confused by some of the ways I've seen the Schrödinger equation written out, I was thinking about making an original post to help others understand the Schrödinger equation as a differential equation, instead of to ask about the Schrödinger equation. Since I got confused by some of the notation, but can now understand it, I can then write it in a way that the maximum number of people can understand how it can be used.

Would this type of original post be off-topic, seeing as its intention would be to help others understand something instead of to seek personal knowledge?

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I was thinking about making an original post to help others understand the Schrödinger equation as a differential equation, instead of to ask about the Schrödinger equation.

PSE posts need to be Q&A. Essentially make the question as if you were actually asking it and didn't know the answer. Then you can make an answer yourself. The post should not just be something aiming to cover your own subjective understanding of the Schrodinger equation; the post should not be something like a blog entry.

Would this type of original post be off topic, seeing as it's intention would be to help others understand something instead of to seek personal knowledge?

While being helpful is typically seen as a necessary condition for a question to stay open, it's not a sufficient one. In addition to the post following the Q&A format, as mentioned above and by QMechanic, you should also make sure the post follows PSE policy.

First, it's hard to tell what the question would actually be from the post here. I see two things you have focused on. Would you be asking about how one should view/understand the terms of the Schrodinger equation? Or would you be asking about how this understanding leads to further understanding of how the equation can be applied?

If both, then I would say a single post would be closed for lacking focus. If you do want to discuss both, I suggest actually making two separate posts, one for each question.

Onto each individual question. The biggest danger I see for the first one is making the question subjective, even if you have an answer prepared for it that the asker (yourself) is looking for. It would be tempting to say something like "what is the best/correct/easiest way to understand the Schrodinger equation and its terms?", but this is a subjective question. Maybe you could ask something along the lines of "What does each term of the Schrodinger equation represent / where does each term come from?" One might argue this is still unfocused since it is asking about each term, but I think overall it's still a single, comprehensive question, so it should be fine.

The second one is a little trickier. A question like, "How can understanding the Schrodinger equation lead to understanding its applications?" would be too broad to have a single answer, and it might be somewhat subjective. Even something like "How is the Schrodinger equation used to approximate the motion of particles through numerical methods?" would still be too broad and unclear IMO, as there are many contexts where this applies, and thus there wouldn't be a single correct answer. You might have to narrow the scope down to a single application: "How is the Schrodinger equation applied in insert context here?" could work as long as you really are focusing on the physics concepts and not the details of the application, such as the numerical methods, etc.

And of course, before you make any question, you should check for duplicate questions. If you find a question that is similar to yours, but you find that the question doesn't sufficiently cover the points you want to ask about, make sure your new question is clearly distinct from it while possibly even addressing that question in your new post if needed. If there is an exact duplicate, but the answer you want to post is not covered in existing answers, you can just post your answer on that question instead. If the answers on the exact duplicate are really poor/non-existent, you might be able to still make your entire Q&A post and then flag your question as the duplicate of the other, thus closing the other post.

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    $\begingroup$ … plus the danger that this becomes an opinion-based or editorial-type question, i.e. what is the OP’s personal understanding of the Schrodinger equation. $\endgroup$ Sep 14 at 16:44
  • $\begingroup$ @ZeroTheHero Yes this is a good point; based on the current version of the meta post it does seem like the OP here is thinking of more of a "blog post" than a Q&A. I'll edit something in to be more clear about this point. $\endgroup$ Sep 14 at 16:48
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Yes, see Do we want and need a set of canonical questions with canonical answers?

I think this needs to be used with care to avoid turning the site into a blog. In the past when I have been contemplating a post like this I have usually asked here if people think the specific post I had in mind would be a useful contribution. The question you describe sounds interesting and I would be interested to see it.

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Well, your posts have to follow the Q&A format of the SE sites.

And yes, you are allowed to self-answer, cf. e.g. this meta post.

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In Q&A format, a thread which is a genuine attempt to share knowledge, but is actually wrong, can be given a better answer by others and the OP's wrong answer down voted. (I'm not talking about trolls or crackpots here - just honest errors).

A "blog post" which doesn't clearly define what question it is asking or answering is harder to fix.

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