Problem 9.1: Identical particles in infinite square well. (25 points) Consider two identical spin-1/2 particles, A and B, of mass m in a one-dimensional infinite square well of length L. Let x4 and xp be the locations of the particles. You may use known results about the infinite square well. For the first two parts, assume the particles don't interact with each other. a) Determine the ground state energy of the two-particle system. Give the associated eigen- state or eigenstates, writing each state as the product of a two-particle spatial wavefunction and a spin state. Is the energy degenerate, and if so what is the degeneracy? b) Determine the first excited state energy of the two-particle system. Give the associ- ated eigenstate or eigenstates, writing each state as the product of a two-particle spatial wavefunction and a spin state. Is the energy degenerate, and if so what is the degeneracy? c) Now imagine the particles are charged. Discuss qualitatively how the ground state energy and first excited state energy changes as a result of the Coulomb potential (you don't have to actually calculate anything). If there is a degeneracy, is it lifted, and which state or states has higher energy? Explain why