Final answer:
The function used to calculate the probability of finding a particle in various regions within a box is the wave function. Its absolute value squared provides the probability density, which can be integrated over a region to find the likelihood of the particle's presence.
Step-by-step explanation:
To calculate the probability of finding a particle in various regions within a box, the function that should be used is the wave function. According to quantum mechanics, the wave function provides a probabilistic description of a particle's position. The absolute value of the wave function, squared, gives us the probability density, which is then integrated over a particular region to find the likelihood of the particle being in that region. Hence, the answer to the question is (a) Wave function.
Essential Knowledge 7.C.1 in quantum mechanics indicates that the wave function can be assigned to an object to describe its motion and interactions, and the absolute value of the wave function is related to the probability of finding a particle in some spatial region. This is different from the classical physics approach, where the probability of finding a classical particle is uniform throughout a box.