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  "body": "\n## Summary\n\nAn unbounded operator is a linear map defined on a linear subspace of a normed space, its domain, with values in another normed space.\nDespite the name, it need not be unbounded: the term means that boundedness is not assumed.\nDifferential operators such as $f \\mapsto f'$ and the position and momentum operators of quantum mechanics are the main examples.\nThe domain is part of the data, and two operators with the same formula but different domains are different.\n\n## Explanations\n\n### L1 human\n\nDifferentiation is a linear operation on functions, but it cannot be applied to every square-integrable function, and it can turn a small function into a huge one.\nFor example, $\\sin(nx)/n$ is small on $[0, \\pi]$, but its derivative $\\cos(nx)$ is not small.\nAn unbounded operator handles this by fixing a domain, a subspace of functions where the operation is defined.\nOn this domain the map is linear, but no bound $\\norm{Tx} \\le C \\norm{x}$ needs to hold.\n",
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