a. Sketch graphs of the probability density | ( x ) | 2 | ( x ) | 2 for the four states

 a. Sketch graphs of the probability density $|\psi \left(x\right){|}^2$ for the four states in the finite potential well of Figure 40.14a. Stack them vertically, similar to the Figure 40.14a graphs of $\psi \left(x\right)$.

b. What is the probability that a particle in the $n=2$ state of the finite potential well will be found at the center of the well? Explain.

c. Is your answer to part b consistent with what you know about standing waves? Explain.

Figure 40.14a:

(a) Finite potential well 1.0 eV E = 0.949 eV Wave function extends into the classically (x) n=4 forbidden region... E3 = 0.585 eV 'n=3 E = 0.263 eV E = 0.068 eV 0 eV- n = 2 n = 1 x (nm) -1 0 1 2 3