theorems:stone-von_neumann

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theorems:stone-von_neumann [2018/05/13 09:18] jakobadmin ↷ Links adapted because of a move operation |
theorems:stone-von_neumann [2018/07/18 13:24] (current) jakobadmin [Intuitive] |
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+ | <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 13:24 by jakobadmin

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