Problem 2.2

Show that \(E\) must exceed the minimum value of \(V(x)\), for every normalizable solution of the time-independent Schrödinger equation. What is the classical analog to this statement? Hint: Rewrite Equation 2.5 in the form

\[\frac{d^2 \psi}{dx^2} = \frac{2m}{\hbar^2} [V(x)-E] \psi;\]

if \(E < V_{min}\), then \(\psi\) and its second derivative always have the same sign – argue that such a function cannot be normalized.

---

Solution: