Exercise 3.1 A particle in an infinite potential box with walls at x = 0 and x = a (i.e., the potential is infinite for x <0 and x>a and zero in between) has the following wave function at some initial time: (x)= 3xx sin (a) Find the possible results of the measurement of the system's energy and the correspond- ing probabilities. (b) Find the form of the wave function after such a measurement. (c) If the energy is measured again immediately afterwards, what are the relative probabili- ties of the possible outcomes?