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# By largely qualitative arguments. Exercise we saw earlier shows that a finite well can hold an $n$th state only if its depth $U_0$ is at least $h^2(n-1)^2 / 8 m L^2$. Show that this result also follows from equation we saw earlier and the accompanying Figure we saw earlier.

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$\textbf{Given Information: }$

\begin{align*} U_0 &= \dfrac{\hbar^2 k^2}{2m} \sec{^2 \dfrac{kL}{2}} \hspace{0.5 cm} (n-1) \pi < kL < n \pi \hspace{0.5cm} \text{odd } n\\ U_0 &= \dfrac{\hbar^2 k^2}{2m} \csc{^2 \dfrac{kL}{2}} \hspace{0.5 cm} (n-1) \pi < kL < n \pi \hspace{0.5cm} \text{even } n \\ \end{align*}

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