Consider a particle in a rigid box of length L. For each of the states n = 1, n = 2, and n = 3:
a. Sketch graphs of |ψ(x)|². Label the points x = 0 and x = L.
b. Where, in terms of L, are the positions at which the particle is most likely to be found?
c. Where, in terms of L, are the positions at which the particle is least likely to be found?
d. Determine, by examining your |ψ(x)|² graphs, if the probability of finding the particle in the left one-third of the box is less than, equal to, or greater than 1/3. Explain your reasoning.
e. Calculate the probability that the particle will be found in the left one-third of the box.