Chapter 38, Problem 66P

To determine

To show:

a) ${\left|\Psi (x,t)\right|}^2=2{{\psi }_0}^2\left[1+\mathit{cos}2kx\right]$

b) The plot of this function and to demonstrate that it describes the square of the amplitude of a standing matter wave.

c) The nodes of this standing wave are located at

$x=(2n+1)\left(\frac{1}{4}\mathrm{\lambda }\right)$, where $n=0, 1, 2, 3, \dots \dots$

d) Expression for the most probable locations of the particle