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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.
Wait, I might be confused here. So my understanding was that:
- The split operator method almost always refers to what's presented in the text as is. That is, a specific method that splits up the operators in a hamiltonian to solve them in their specific spaces. The split-step Fourier method is the same algorithm under a different name
- The split-step method (without the Fourier distinction) is as you say, a general class of algorithms that can be used in a variety of different situations.
Maybe I need to further improve this, and I've over-genericised the text.
If I'm honest, I was a little... What? while reading this, so I was trying to simplify from a process of collating a few sources.
- Accelerating the Fourier split operator method via graphics processing units
- OPERATOR SEPARATION OF VARIABLES FOR ADIABATIC PROBLEMS IN QUANTUM AND WAVE MECHANICS
- Noisy intermediate-scale quantum simulation of the one-dimensional wave equation
- Quantum Lattice Boltzmann is a quantum walk
- Hamiltonian formulation and symplectic split-operator schemes for time-dependent density-functional-theory equations of electron dynamics in molecules
I'd welcome feedback if I've made the text harder to understand, or misunderstood any of the materials, because I am not a quantumn theoretical computer scientist, or theoretical physicist