http://grephysics.net/ans/8677/96

ok i am totally confused with this.. if V +V' is even then eigenfunctions will be either even or odd, but then how can we say about the disappearance of the odd terms using symmetry, yosun also used symmetry arguments to solve 9677#98 http://grephysics.net/ans/9677/98, griffith has never used it explicitly, can anyone refer some notes or books for symmetry?