Answer
See explanation.
Work Step by Step
According to classical physics, the particle should be trapped in the finite well. However, quantum mechanics allows the wavefunction to penetrate into the classically forbidden region. The greater the particle’s energy, the greater the chance that it will be found outside the well, so the wavefunction extends farther out of the well.
Mathematically, equation 40.40 gives the wavefunction outside the well, and an equation just like 40.42 gives the value of $\kappa$.
We see that if E is close to the barrier height $U_o$, the wavefunction has a larger value, which confirms our physical intuition.
