Two non-interacting particles are in the 1-dimensional infinite square well which has the width a. Assume that one particle is in state labeled by n1 = 1 (ground state) and the other is in the first excited state n2 = 2.

{5 points) Two noninteracting particles are in the ldimensional innite square well which has the width {1. Assume that one particle is in state labeled by R] = 1 [ground state) and the other is in the rst excited state T12 = 2. What are the possible wave functions if : a) particles are distinguishable b] particles are indistinguishable. Construct symmetric and antisymmetric wave functions. Evaluate explicitly the expectation value of ([591 1:2)2} using these wave nlctions