I once spent around ten weeks writing a C program to numerically integrate the Schrödinger equation for an electron in a particular magnetic field. When I started looking at results, they looked eerily like trig functions. A little digging revealed that the problem was stated and solved (exactly) in one of the exercises to Quantum Mechanics by Landau and Lifshitz.

I sheepishly told my advisor at the time what had happened, worried he would think me an idiot, but he was thrilled: "You solved the problem! That's what's important."