Finite Square well problem

An electron is confined to a finite square well whose “walls” are $8.0$ eV high. If the ground-state energy is $0.5$ eV, estimate the width of the well.

My solution:

$E_1=0.5 \ eV=8\times10^{-20} \ J$

Electron mass: $m=9.11\times10^{-31} \ Kg$

$\hbar=1.055\times 10^{-34} \ Js$

$E_1=\frac{\pi^2 \hbar}{2mL^2} \ \Rightarrow \ L=\frac{\pi\hbar}{\sqrt{2mE_1}}=\frac{\pi(1.055\times 10^{-34} \ Js)}{\sqrt{2(9.11\times10^{-31} \ Kg)(8\times10^{-20} \ J)}}=8.6813\times 10^{-10} \ m\approx 0.87 \ nm$

This is a problem from Modern Physics, Paul A. Tipler / Ralph A. Llewellyn, and when I check solution in Answers section at the end of the book, I found that it is the same answer that I found.

But, my T.A. told me I can't do this because I'm apllying concepts for Infinite Square Well (equation for $E_1$). I thought I can do this because $E_1<V_0$ and does not matter if $V_0\rightarrow\infty$, $E_1$ is still under $V_0$.

What am I understanding wrong?

How can I find answer without using quation for $E_1$ that I already use?

• – Gert Nov 24 '16 at 17:03

As soon as $E_1 < \infty$, you cannot assume $\Psi = 0$ outside the well anymore. In other words, your formula doesn't work because the wave function "leaks into" the walls of the well (tunneling).