7.1 Exercise 13

A wave function of a particle with mass m is given by

$\psi \left(x\right) = \left\{\right. \begin{aligned}A \text{cos} \alpha x , & - \frac{\pi}{2 \alpha} \leq x \leq + \frac{\pi}{2 \alpha} , \\ 0 , & \text{otherwise},\end{aligned}$

where $\alpha = 1.00 \times 10^{10} / \text{m}$. (a) Find the normalization constant. (b) Find the probability that the particle can be found on the interval $0 \leq x \leq 0.5 \times 10^{−10} \text{m}$. (c) Find the particle’s average position. (d) Find its average momentum. (e) Find its average kinetic energy.