Question

Please solve with full explanation

Answer 1

Refer to attachment!

:-)

Answer 2

Answer:

common situation which pops up when dealing with commutators of operators. On an appropriate space of functions $\mathcal D$ (like an $L^2$-space or the Schwartz space etc...), the operators $x$ and $p$ are given by

$$x(f)(x):=xf(x), $$ $$p(f)(x):=\frac{h}{i}\frac{df}{dx}, $$

for all $f\in \mathcal D$ and $x$ in the domain of $f$. In other words, $x(f)$ and $p(f)$ are elements in $\mathcal D$, i.e. functions. In particular $\frac{df}{dx}$ is the derivative of $f$ w.r.t. $x$ at the point $x$, by convention.

The commutator