Answer
Always try to find the normalization constant $A$ to solve such problems as done below. In part (c) it is asked to find the expectation value of $x$, $ x^{2}$ , $p$ and $p^{2}$. Obviously, $\lt$$\psi$|$x$|$\psi$$\gt$ = 0 as the function inside the integral will be an odd function of $x$ and integrand of an odd function over a symmetric interval (-$\infty$ to $\infty$) is zero. Similarly the momentum operator $\hat{p}=-i\hbar$$\frac{d}{dx}$ when acted on $\psi$ will give an odd function of $x$, which when multiplied by $\psi$*(which is an even function of $x$) will give an odd function. This odd function on integration over symmetric interval (-$\infty$ to $\infty$) will give zero.
Work Step by Step
In part (d), $\sigma$$_{x}$ is standard deviation in position operator $x$ which is given below:
$\Delta x=\sqrt {- ^{2}}$
As =0, so $\Delta x=\sqrt {}$.
