This is the third article in a series dedicated to examining the use of the delta function in the physics literature. Here we discuss the appearance of a delta function in the second derivative of the wave function if its derivative is discontinuous. When this happens it is often claimed in the literature that the proposed wave function must be eigenfunction of an operator that contains a delta function and, in some cases, it is rejected. We study in this paper what we believe are alternatives ways to deal with this situation.
Keywords:
Dirac delta function; time independent Schrodinger equation