Solution
= Solution
As $|x|\to\infty$, the equation approaches
$$
\chi''+\frac{2m}{\hbar^2}(E-U_0)\chi=0.
$$
If $E>U_0$, the asymptotic solutions are oscillatory and do not decay, so there are no <bound states>. If $0<E<U_0$, the asymptotic solutions are exponential; one decaying branch can be selected at each end. <Bound states> are therefore possible, although only energies satisfying the global matching conditions actually occur.