Calculate the commutator [p x , x[SUP]n[/SUP]]

[hanspl]

Calculate the commutator [p_x, xⁿ]

Homework Statement

There are 3 tasks.
1) No other information is given. only that I have to calculate the commutator [p_x, xⁿ].

For task 2 and 3 a relevant equation is given below.

2) calculate the commutator [x, K_x]

3) calculate the commutator [p_x, K_x]

Homework Equations

We define the kinetic energy operator of a particle in one dimension (x) as

K_x = - (h(hatch)²/2m)(d²/dx²)

I hope anyone can help me. I am really stuck with these commutators.

- HP

 

[Catria]

Try multiplying the commutator at the right by some phantom ket |K>...