1. Consider a particle of mass m in an infinite square well with potential energy 0 for 0 Sz S a oo otherwise V (x) For simplicity, we may take the ‘universe’ here to be the region of 0 S z S a, which is where the wave function is nontrivial. Consequently, we may express stationary state n as where En is the associated mechanical energy. It can be shown that () a/2 and (p:)0 for stationary state n. (a) Calculate the mean values (2) and (p2) for stationary state n. (b) Calculate the rms deviations Oz, and ơP. for stationary state n. Check that the Heisenberg uncertainty principle is satisfied. Which state comes closest to the uncertainty limit?