Quantum Mechanics is an incredibly difficult subject to understand, even to physicists. To obtain solutions in the field of Quantum Physics, and hence to be able to make predictions in the physical world, there are two different mathematical methods that are utilized. However, it is not obvious that these two methods are actually equivalent, since they are incredibly different both visually and mathematically. One way of tackling tough problems in Quantum Mechanics, is by utilizing the more intuitive branches of math which are Calculus and Differential Equations. Although it helps understand the problem more, it is significantly more time consuming than using the Linear Algebra approach, which involves matrices and operators. Again, it is not obvious that these methods are actually the same, so I set out to prove it once and for all. This past summer, I proved that these two methods are indeed equivalent by solving the Hydrogen atom wavefunction using both of these methods, proving by construction that these two methods are indeed equivalent.