Let be two 12 spin particles, with their spin operators given by S1 and S2. A possible base formed by S1^2, S2^2, Slz and S2z self-states, represented by {Iml, m2}. (a) Let the Hamiltonian of interaction between these particles be given by H=-J * Slz * S2z, where J is a positive constant. Find the H0 eigenvalues and eigenstates. Draw the level diagram of energy and point out the degeneration if any. (b) Find the vectors of the base of self-states of Si^2, S2^2, S^2 and Sz in terms of {]ml, m2} (c) Let now be the Hamiltonian of interaction between these particles given by H Heisenberg = -J* S1.S2, where J is a positive constant. Find the H0 eigenvalues and eigenstates. Draw the diagram of energy levels and point to degeneration if any. Let be two 12 spin particles, with their spin operators given by S1 and S2. A possible base formed by S1^2, S2^2, Slz and S2z self-states, represented by {Iml, m2}. (a) Let the Hamiltonian of interaction between these particles be given by H=-J * Slz * S2z, where J is a positive constant. Find the H0 eigenvalues and eigenstates. Draw the level diagram of energy and point out the degeneration if any. (b) Find the vectors of the base of self-states of Si^2, S2^2, S^2 and Sz in terms of {]ml, m2} (c) Let now be the Hamiltonian of interaction between these particles given by H Heisenberg = -J* S1.S2, where J is a positive constant. Find the H0 eigenvalues and eigenstates. Draw the diagram of energy levels and point to degeneration if any