1. The problem statement, all variables and given/known data A system consists of two indistinguishable spin-1 fermions, both confined inside the same box of length L centred on the origin. The particles do not interact with each other. a) What is the total energy of the ground state of this system? (Use the standard formulas for the energy eigenvalues of a single particle in a box.) b) What is the spin angular momentum of the system in the ground state? c) How many distince and mutually orthogonal space-spin energy eigenstates of the whole system are there in which there is one particle in the single-particle ground state and one particle in the single-particle first exctied state? Choosing these eigenstates so that they are also eigenvectors of the square and the z-component of total spin angular momentum, write explicit formulas for all these space-spin eigenstates. (Use alpha, beta notation for spin-up and spin-down states.) d) With no interaction between the particles, the energy eigenstates described in part c) all have exactly the same energy (they are degenerate). We now introduce a repulsive interaction between the two particles. Describe the qualitative effect that this interaction has on the relative energies of the singlet and triplet eigenstates. 3. The attempt at a solution a)E(subscriipt n)=(h^2 n^2)/(8mL^2) there are 2 spin 1 fermions, n=1, so the total energy is=(h^2)/(3mL^2) b)spin angular momentum=(1/2)+(1/2)=1 =(1/2)+(-1/2)=0 is this also possible? =(-1/2)+(-1/2)=-1 is this also possible? I haven't tried c and d yet. But I just wanted to check that I got questions a and b right because I am worried that I have misunderstood que a and b. Thank you if you reply.