I am an undergraduate studying quantum physics with the book of Griffiths. in 1-D problems, it said a free particle has un-normalizable states but normalizable states can be obtained by sum up the solutions to independent Schrodinger equations. in my view the book also suggests that a scattering state with E>V(infinity) is to be un-normalizable. Is it true in 1-D situations? If so can it be generalized to 3-D situations? And why?