Shallow finite-square-well energy
= Shallow finite-square-well energy
{title2=$E_0\simeq-2mV_0^2a^2/\hbar^2$}
For a well of depth $V_0$ and full width $2a$, measured from zero exterior <potential energy>, even-state matching gives $q=k\tan ka$. If $a\sqrt{mV_0}/\hbar\ll1$, then $ka\ll1$ and $q\simeq2mV_0a/\hbar^2$. Using $E_0=-\hbar^2q^2/(2m)$ gives the displayed leading binding <energy>. It agrees with the attractive delta-potential result for integrated strength $2aV_0$.