Euler's first claim to fame was solving the Basel problem, which required him to calculate that $\zeta(2)$ was $\frac{\pi^2}{6}$; since Euler's time, mathematicians have found a closed form for the zeta function evaluated at all the even positive integers. This problem provides a rare opportunity to directly apply the results of physics to a problem in pure math. After a brief introduction to quantum mechanics, I will use the physics of the infinite square well (also called the particle in a box) to give a method for computing the zeta function at the even positive integers, reducing the problem to the evaluation of certain elementary integrals.