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
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 6, 2018 at 3:31 | comment | added | user171780 | I have found the answer to my previous question here. | |
| Aug 6, 2018 at 3:13 | comment | added | user171780 | How did you found that $[p,x^j] =-i \hbar jx^{j-1}$? | |
| Oct 19, 2017 at 18:10 | vote | accept | John Doe | ||
| Oct 19, 2017 at 18:10 | comment | added | John Doe | I did it: $$F(x)=\sum_{j=0}^\infty f_j x^j;$$$$\begin{align} [p,F(x)]&=\sum_{j=0}^\infty f_j[p,x^j]\\ &=-i\hbar\sum_{j=0}^\infty f_j jx^{j-1}\\ &=-i\hbar\sum_{j=0}^\infty f_j \frac\partial{\partial x} x^j\\ &=-i\hbar \frac\partial{\partial x} \sum_{j=0}^\infty f_jx^j\\ &=-i\hbar \frac{\partial F(x)}{\partial x}\end{align}$$ Thanks! | |
| Oct 19, 2017 at 18:07 | history | edited | tparker | CC BY-SA 3.0 |
added 6 characters in body
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| Oct 19, 2017 at 17:56 | history | answered | tparker | CC BY-SA 3.0 |