Coupled spin-1/2 particles [8 marks] suppose we have two spin-1/2 particles, with associated spin operators sı and s2. the simultaneous eigenstates of siz and s2. are mi, m2), which we can write as the spins interact with each other, such that the two-prid hamitonian i (2.2) where is a real constant (with units of energy divided by ћ2). (a) does the hamiltonian (2.2) have rotational symmetry? justify your answer. (b) show that it, and iļ. l) are eigenstates of the hamiltonian (2.2), and determine their energy eigenvalues (c) determine the remaining energy eigenstates that involve the states it, ) and |,) along with the corresponding energy eigenvalues (d) for α > 0, identify the ground state and discuss whether or not it is entangled. how do your results change when α < 0?