Approximations · [Apr 4, 08:19 PM]
I have promised myself never choose to work on anything that involves approximating operators. Here is how badly you might suffer if you worked on approximations involving operators:
- If any of the operators is not bounded, it might even not have a spectrum. You can not even safely multiply it by another one, let alone use expansions with it.
- Chain rule can take a nasty form when applied to operators.
- Expansions such as the BCH (Baker-Campbell-Hausdorff) expansion are only valid for bounded operators with a domain of convergence set by the algebraic properties of the operators involved.
- Approximating unitary operators is hard because their eigenvalues are distributed on a circle instead of a line.
- No one can understand what you’ve done.
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