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.
