Chapter 41, Problem 41.53P

(a)

To determine

To show: For an excited state of hydrogen, the smallest angle the orbital angular momentum vector $\overrightarrow{L}$ can have with the $z$-axis is

${\left({\theta }_L\right)}_{\min }=\arccos \left(\frac{n-1}{\sqrt{n\left(n-1\right)}}\right)$.

(b)

To determine

The largest possible angle, ${\left({\theta }_L\right)}_{\max }$ between $\overrightarrow{L}$ and the $z$-axis.