From d4c66ff697069736e6d4faa926ce909f0ed3583f Mon Sep 17 00:00:00 2001 From: Lewis Cowles Date: Sat, 15 Feb 2025 01:17:45 +0000 Subject: [PATCH 1/2] docs: improve split-operator documentation I've added a high level description which I think better classifies and summarises this approach to solving a problem. I've used the term meta algorithm, because this can be applied to a wide number of problems, with different, contextual and situational concrete algorithms. --- contents/split-operator_method/split-operator_method.md | 6 +++++- 1 file changed, 5 insertions(+), 1 deletion(-) diff --git a/contents/split-operator_method/split-operator_method.md b/contents/split-operator_method/split-operator_method.md index 08fc3d33d..95cbd8ab7 100644 --- a/contents/split-operator_method/split-operator_method.md +++ b/contents/split-operator_method/split-operator_method.md @@ -1,5 +1,9 @@ # 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. + +It describes a way of decomposing complex problems into smaller, more manageable subproblems, which can then be solved iteratively or in parallel. + +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): $$ From c8ff24ea300b959ce106f4893032f434515d1a0b Mon Sep 17 00:00:00 2001 From: Lewis Cowles Date: Sun, 16 Feb 2025 19:13:09 +0000 Subject: [PATCH 2/2] docs: review feedback Co-authored-by: James Schloss --- contents/split-operator_method/split-operator_method.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/contents/split-operator_method/split-operator_method.md b/contents/split-operator_method/split-operator_method.md index 95cbd8ab7..4c1ea9ae0 100644 --- a/contents/split-operator_method/split-operator_method.md +++ b/contents/split-operator_method/split-operator_method.md @@ -1,7 +1,7 @@ # The Split-Operator Method 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. -It describes a way of decomposing complex problems into smaller, more manageable subproblems, which can then be solved iteratively or in parallel. +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):