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  "body": "\n## Summary\n\nA rigged Hilbert space, or Gelfand triple, is a chain $\\Phi \\subset H \\subset \\Phi'$.\nHere $H$ is a Hilbert space, $\\Phi$ is a dense subspace with a finer topology, and $\\Phi'$ is the dual of $\\Phi$.\nIt gives a rigorous home to objects such as the Dirac delta and plane waves, which are not vectors of $H$.\nWith a nuclear space $\\Phi$, it carries the spectral theorem in terms of generalized eigenvectors.\n\n## Explanations\n\n### L1 human\n\nQuantum mechanics likes to speak of states of exact position, but such states are not square-integrable functions.\nA rigged Hilbert space adds a small space of very nice functions and a large space of generalized functions around the Hilbert space.\nThe usual example is Schwartz functions inside $L^2(\\R)$ inside tempered distributions.\nThe delta function $\\delta_a$ lives in the large space and is an eigenvector of the position operator there.\n",
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