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docs: improve split-operator documentation #1024

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docs: improve split-operator documentation #1024

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docs: improve split-operator documentation
Lewiscowles1986 Feb 15, 2025
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docs: review feedback
Lewiscowles1986 Feb 16, 2025
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6 changes: 5 additions & 1 deletion contents/split-operator_method/split-operator_method.md
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# The Split-Operator Method
The Split-Operator Method (also called the Split-Step Method), was actually the primary method I used to solve the Schrödinger equation during my PhD.
The Split-Operator Method (also called the Split-Step Method) can be best understood, as a problem-solving approach or meta-algorithm rather than a standalone algorithm, which solves a single problem.
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I think I am understanding where you are coming from this statement. I see some of the references still had operator splitting, but did not specifically use the Split-step fourier method. Even though in practice the SSFM is the most common approach used for the split operator method, I think it should be made more explicit in the text that there is a difference between these approaches.

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So I have a question here. Should I make the change in my branch to call this, "split-step fourier method", or have I really just taken us both down a rabbit hole which is unhelpful?

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@leios leios Feb 16, 2025 •
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Can I come back to this? I think what might happen is that I will create a new PR that is co-authored with you with the necessary changes. This discussion is a good one, I just have to rethink about how to package it.

It'll take like 10 minutes, but I might not have that time available until later this week.

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its not urgent to me. This was sort of me thinking I was helping, but maybe I'm not

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For the record, the conversation is definitely helpful! Thanks


It describes a way of decomposing a physical equation of energy into different subspaces where it is easier to find solutions.

This was the primary method I used to solve the Schrödinger equation during my PhD.
It is one of the simplest and fastest methods for this purpose and is widely used throughout modern quantum research in the area, in particular when dealing with the Non-linear Schrödinger Equation (NLSE):

$$
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