In this video my goal is to completely solve the Finite Square Well problem in Quantum Mechanics. The task is to look for the bound state and unbound state solutions via solving the Schrodinger's equation for both inside and outside the walls of the well and will do so via the graphical solution to the transcendental equation and will discuss the solutions with their dependence on the size of the potential and the width of the well, we shall also see that there is at least always one bound state despite how small the value for potential is.