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--- theorems:stone-von_neumann [2018/05/02 09:11]
jakobadmin [Intuitive]
+++ theorems:stone-von_neumann [2018/07/18 13:24]
jakobadmin [Intuitive]
@@ Line 3: / Line 3: @@
 <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>
 <blockquote>In typical physics quantum mechanics textbooks, one often sees calculations
-made just using the [[equations: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
 representation of the operators that satisfy these relations. This turns out
 to be justified by the remarkable fact that, for the Heisenberg group, once one