In class, we evaluated the normalization constant for the particle-in-a-box wave function by insisting that the probability of finding the particle somewhere in the box (i. e., between 0 and L) is 1. The same type of integral can be used to evaluate the probability of finding the particle in some interval within the box. a) Find an expression for the probability of finding the particle between L/3 and 2L/3, i. e., in the middle third of the box.

b) Evaluate your expression for n=1.

c) Evaluate your expression in the limit as n = infinity. This is called the “classical limit”. It is a general feature of quantum mechanics that, in the limit of high quantum numbers, behavior approaches that of classical mechanics. What would you expect classically for the probability of finding the particle in the middle third of the box? Does your quantum mechanical result match this in the limit as n approaches infinity?