Chapter 40, Problem 40.2E

(a)

To determine

The two smallest positive values of $x$ for which the probability function at $t=0$ ${\left|\Psi \left(x,t\right)\right|}^2$ is a maximum.

(b)

To determine

The two smallest positive values of $x$ for which the probability function at $t=2\pi /\omega$ ${\left|\Psi \left(x,t\right)\right|}^2$ is a maximum.

(c)

To determine

$v_{\text{av}}$ as the distance the maxima have moved divided by the elapsed time and to compare the result to the expression $v_{\text{av}}=\left({\omega }_2-{\omega }_1\right)/\left(k_2-k_1\right)$.