Learning Goal: To use the wave function for a particle in a box to calculate the probability that the particle is found in various regions within the box. The quantum mechanical probability that a particle described by the (normalized) wave function 111(1) is found in the region between :1: : a and a: : b is P = f: l'cl:(a:)|2d:c. The specic example of a particle trapped in an infinitely deep potential well. sometimes called a particle in a box, serves as good practice for calculating these probabilities, because the wave functions for this situation are easy to write down. If the ends of the box are at z : 0 and a: : L, then the allowed wave functions are 2 ' m