A quantum particle placed in a hard -wall box (i.e., a rectangular potential well of infinite depth) of width a is in the state described by the wave function (x) {(a/2)2 x2, |x| < a/2 , 0, |x| > a/2 . Find the probability P that a measurement of energy will find the lowest possible value. (As you will discover, P is very close to 1.) For reference: the ground state wave function for a particle in a hard -wall box reads 0(x) |x|