Rather, the lowest energy state must have the minimal amount of bending of the wavefunction necessary for it to be zero at both walls but nonzero in between -- this corresponds to half a period of a s...Rather, the lowest energy state must have the minimal amount of bending of the wavefunction necessary for it to be zero at both walls but nonzero in between -- this corresponds to half a period of a sine or cosine (depending on the choice of origin), these functions being the solutions of Schrödinger’s equation in the zero potential region between the walls.