A particle of mass m is confined inside an infinite well with a Potential Energy giver V(x) = for 10o for x a The particle has a normalized wave function given by V(x, () = - VZ + 42(x)ein /2 a. Using the fact that for an infinite well the w are real functions, show that t probability distribution |P(x, ) -= *(x, /) P (x, f) is equal to: | 4(x,D = = (4,(x)) += (42(1)) + 4,(x)4/2(x) cos 3E b. Using the the result in a. for |I(x, /) and the orthonormality properties of the eigenfunctions, show that 00 [14(x,1)| dx = 1 -00