operator with eigenvalue . We write the eigenvalue equation in position coordinates,

recalling that simply multiplies the wave-functions by the function , in the position representation. Since the function is variable while is a constant, must be zero everywhere except at the point . Clearly, no continuous function satisfies such properties, and we cannot simply define the wave-function to be a complex number at that point because its -norm would be 0 and not 1. This suggest the need of a "functional object" concentrated at the point