Timeline for Commutator of $[\hat p, F(\hat x)]$ without using $\hat p=-i\hbar\frac\partial{\partial x}$?
Current License: CC BY-SA 3.0
5 events
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| Oct 20, 2017 at 16:09 | comment | added | Luke Pritchett | I have edited my answer to make it slightly clearer the distinction between the abstract generator of translations and the differential operator $-i\partial_x$. In any case, the statement that $[x,p]=i\hbar$ is exactly equivalent to the statement that $p$ generates translations. | |
| Oct 20, 2017 at 16:07 | history | edited | Luke Pritchett | CC BY-SA 3.0 |
Added detail on meaning of generator of translations.
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| Oct 19, 2017 at 22:52 | comment | added | John Doe | @ZeroTheHero I think you may have misread what I wrote - we have defined $p$ in this way. I just didn't want to use the fact that $p=-i\hbar \frac\partial{\partial x}$. | |
| Oct 19, 2017 at 20:28 | comment | added | ZeroTheHero | The OP wishes to prove without using the fact that $p$ generates translations... | |
| Oct 19, 2017 at 17:59 | history | answered | Luke Pritchett | CC BY-SA 3.0 |