Matching boundary conditions for a square well (E < 0), we find that there are only certain energies for which there is a solution to the Schrodinger equation which decays exponentially outside the well. These are the bound states. One can graphically solve for the energy of these states. For the one dimensional square well there is always at least one solution. The deeper the well, the more bound states there will be. For an infinite square well, there is an infinite number of bound states, which satisfy the boundary condition that the wave function vanishes at the sides of the well. The bound state wave functions alternate between even and odd parity.