Timeline for Universal $C^*$-algebra with generators and relations
Current License: CC BY-SA 3.0
3 events
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| Jul 15, 2014 at 13:30 | comment | added | Phoenix87 | As an application of this in Quantum Mechanics, one can consider the position and momentum operators $x$ and $p$, which, according to the standard quantization, must satisfy $xp - px \subset 1$ (assuming natural units, where $\hbar = 1$). Then the above argument shows that $x$ and $p$ cannot be bounded operators. To deal with bounded operators one can do the Weil trick to take the exponentials $e^{i\xi p}$ and $e^{i\eta x}$ in order to get unitaries through Borel functional calculus. | |
| Dec 15, 2013 at 23:35 | history | edited | Sebastien Palcoux | CC BY-SA 3.0 |
I've added that this relation is well-known and is called Heisenberg relation.
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| Dec 15, 2013 at 11:40 | history | answered | Sebastien Palcoux | CC BY-SA 3.0 |