What Is the Result of the Commutator [x,T] in Quantum Mechanics?

[kq6up]

Homework Statement

Find $[\hat{x},\hat{T}]$.

Homework Equations

$[\hat{x},\hat{T}]=\hat{x}\hat{T}-\hat{T}\hat{x}$

The Attempt at a Solution

I wind up with $\frac{i\hbar}{m}\hat{p}$. Did I do good, boss?

Chris

 

[Dr Transport]

Define $\hat{T}$

 

[kq6up]

It is the kinetic energy operator. p^2/2m.

Chris

 

[CAF123]

Your answer is correct.

I am not sure if this is the way you did it, but using the fact that $[A,BC] = B[A,C] + [A,B]C$ for operators $A, B$ and $C$, the result follows in one line using the canonical commutation relations for $\hat{x}$ and $\hat{p}$.