4 ms·
If you can map non-linear eq's to linear, i.e. Schrodinger eq, doesn't that dramatically reduce computation required? Non-linearity is necessary for chaos. This
by meroes 6y ago
If you can map non-linear eq's to linear, i.e. Schrodinger eq, doesn't that dramatically reduce computation required? Non-linearity is necessary for chaos. This seems like a big deal to an layman like me. I don't know how it's done, but isn't the fact that nonrelativistic QM and classical mechanics are nearly identical at certain scales enough to say a mapping can be done.
- rowanG077 6y agoDid you read the article? It's possible to write a non-linear equation as an infinite set of lineair ones. They use this fact in one of their solutions.
- ur-whale 6y agoThe mapping is not 1-to-1, it's done via approximation, which means that what gets solved is not the original equation. And ... as I believe poincaré found out when he tried to apply series expansion to the 3 body problem, the devil (chaotic behavior) is in the long tail of the series coefficients [edit]: https://en.wikipedia.org/wiki/Poincar%C3%A9_and_the_Three-Body_Problem https://en.wikipedia.org/wiki/Poincar%C3%A9_and_the_Three-Bo... http://www.bourbaphy.fr/chenciner.pdf http://www.bourbaphy.fr/chenciner.pdf