Question

Figure 40.15a shows that the higher the energy of a bound state for a finite potential well, the more the wave function extends outside the well (into the intervals $x\to 0$ and $x\to L$). Explain why this happens.

Short answer

answer is not given in the document

Step-by-step solution

The mathematical solution of wave function for finite well

The solution of the wave function for outside the finite well is given by

$\psi \left(x\right)=C{e}^{kx}+D{e}^{-kx}$

Where $k=\sqrt{2m(U_0-E)/h^2}$

Explanation

If the energy of bound state E is greater than a $U_0$ bounded potential then k becomes exponential which causes the wave function to extend more outside the well.