Chapter 9.1, Problem 9.2P

(a)

To determine

Show that $i\hslash f"-{\left(f\text{'}\right)}^2+p^2=0$ when substituting the given wave function into Schrödinger’s equation.

(b)

To determine

Show that ${\left(f_0^{\text{'}}\right)}^2=p^2$, $i{f}_0^{"}=2f_0^{\text{'}}{f}_1^{\text{'}}$, $i{f}_1^{"}=2f_0^{\text{'}}{f}_2^{\text{'}}+{\left(f_1^{\text{'}}\right)}^2$, etc.

(c)

To determine

The expression for $f_0\left(x\right)$ and $f_1\left(x\right)$ and show that the first order in $\hslash$ recover Equation 9.10.