quantum operators algebra

1. The problem statement, all variables and given/known data

Hi,guys. I have a hard time understanding algebra and tricks of operators.

So i have few examples:

1)[[itex]\hat{p}[/itex]²_x,xⁿ]

2)[[itex]\hat{l}[/itex]_z,x],where [itex]\hat{l}[/itex]_z=x[itex]\hat{p}[/itex]_y-y[itex]\hat{p}[/itex]_x

2. Relevant equations







3. The attempt at a solution

1)[[itex]\hat{p}[/itex]²_x,xⁿ]=

[[itex]\hat{p}[/itex]_x [itex]\hat{p}[/itex]_x,xⁿ]=

[itex]\hat{p}[/itex]_x[[itex]\hat{p}[/itex]_x,xⁿ]+[[itex]\hat{p}[/itex]_x,xⁿ][itex]\hat{p}[/itex]_x

So xⁿ is not a operator,i dont know what i should do next?



2)[[itex]\hat{l}[/itex]_z,x],where [itex]\hat{l}[/itex]_z=x[itex]\hat{p}[/itex]_y-y[itex]\hat{p}[/itex]_x

Some tips or ideas here ?





1. The problem statement, all variables and given/known data







2. Relevant equations







3. The attempt at a solution

1. The problem statement, all variables and given/known data







2. Relevant equations







3. The attempt at a solution

1. The problem statement, all variables and given/known data







2. Relevant equations







3. The attempt at a solution

1. The problem statement, all variables and given/known data







2. Relevant equations







3. The attempt at a solution

1. The problem statement, all variables and given/known data







2. Relevant equations







3. The attempt at a solution