- #1
elmp
- 2
- 0
can someone please help me with this. it's killing me.
to show [tex]\left[\vec{L}^{2}\left[\vec{L}^{2},\vec{r}\right]\right]=2\hbar^{2}(\vec{r}\vec{L}^{2}+\vec{L}^{2}\vec{r})[/tex]
I have already established a result (from the hint of the question) that
[tex]\left[\vec{L}^{2},\vec{r}\right]=2\imath\hbar\vec{r}\times\vec{L}+2\hbar^{2}\vec{r}[/tex]
but where to go from that?
basically I will need to show either one of (4.55) from http://www.eng.fsu.edu/~dommelen/quantum/style_a/commute.html, but I am running out of clues.
Homework Statement
to show [tex]\left[\vec{L}^{2}\left[\vec{L}^{2},\vec{r}\right]\right]=2\hbar^{2}(\vec{r}\vec{L}^{2}+\vec{L}^{2}\vec{r})[/tex]
Homework Equations
I have already established a result (from the hint of the question) that
[tex]\left[\vec{L}^{2},\vec{r}\right]=2\imath\hbar\vec{r}\times\vec{L}+2\hbar^{2}\vec{r}[/tex]
but where to go from that?
The Attempt at a Solution
basically I will need to show either one of (4.55) from http://www.eng.fsu.edu/~dommelen/quantum/style_a/commute.html, but I am running out of clues.