I need help with the electron spin wavefunctions and normalization. Please show steps.

Show transcribed image text 1) The electron spin wave functions form a complete, orthonormal set of functions, meaning where a(i) and B(i) are the spin up and spin down wave functions for electron i. Consider the spin wave function sigma+, defined in class as sigma+= (1/2)^1/2 [a.(1)B(2) + B(1)a(2)] a) Show that sigma + is a correctly normalized spin wave function. b) Show that c is orthogonal to the spin wave function a(1)a(2).