In Classical Mechanics

In figure 20.1 we show a general potential $V(x)$.

Figure 20.1:

A particle of energy $E$ moving in this potential has momentum $p$ which is given by

$$\frac{p^2}{2m} + V(x) = E$$ (20.43)

or

$$p= \pm \sqrt{2m (E - V(x))}$$ (20.44)

Since $p$ is real we can see that the particle's motion is restricted to the region where $E \ge V(x)$, or the region  $x_a \le x \le x_{_b}$ shown in the the figure. In the same situation, what happens in Quantum Mechanics?