Chapter 12, Problem 14E

(a)

To determine

To show: ${\Psi }_1(x,t)=A{e}^{ikx-i\omega t}$ is the solution of both Klein-Gordon and the Schrodinger equations.

(b)

To determine

To show: ${\Psi }_2(x,t)=A{e}^{ikx}\cos \omega t$ is the solution of both Klein-Gordon but not the Schrodinger equations.

(c)

To determine

To show: The ${\Psi }_2$ is a combination of positive and negative energy solutions of the Klein-Gordon equation.

(d)

To determine

To compare: The time dependence of $|\Psi {|}^2$ for ${\Psi }_1$ and ${\Psi }_2$