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theorems:stone-von_neumann

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theorems:stone-von_neumann [2018/05/13 07:18]
jakobadmin ↷ Links adapted because of a move operation
theorems:stone-von_neumann [2018/07/18 11:24] (current)
jakobadmin [Intuitive]
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 <tabbox Intuitive> ​ <tabbox Intuitive> ​
 +<​blockquote>​The Stone-von Neumann theorem roughly says that for any operators $A$ and $B$ satisfying the canonical commutation relation, we can get away with using the standard representation $A \rightarrow u,\ B \rightarrow -i \hbar \frac{d}{du}$ without loss of generality. (More precisely, it says that any representation of the *exponentiated* canonical commutation relation on a sufficiently smooth Hilbert space is unitarily equivalent to the standard representation,​ so any other representation basically just describes the same physics in a different coordinate system.)<​cite>​https://​physics.stackexchange.com/​a/​264587/​37286</​cite></​blockquote>​
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 <​blockquote>​In typical physics quantum mechanics textbooks, one often sees calculations <​blockquote>​In typical physics quantum mechanics textbooks, one often sees calculations
 made just using the [[formulas:​canonical_commutation_relations|Heisenberg commutation relations]],​ without picking a specific made just using the [[formulas:​canonical_commutation_relations|Heisenberg commutation relations]],​ without picking a specific
theorems/stone-von_neumann.txt · Last modified: 2018/07/18 11:24 by jakobadmin