Interacting Spin$-1/2$ ParticlesPH$3101$A system of two spin$-$ particles with spin operators $$1$ and $52$ can be deseribed byan effective Hamiltonian:H$-=$ A$($$$1$z$+$ $$2$z$)+$ B$$,.$$$2,$where A and B are real constants$($a$)$ Find the energy levels of A$.($b$)$ The total angular momentum is S $=$ $$,+$ $$2.$ Find the matrix representation of Ain the $|$S$15$ S$2$i S$,$ m$)$ basis.$($c$)$ Write the $|$$$1,$ $$2$; s$,$m$)$ states in terms of the $|$s$1,$ sz; m$4,$ m$2)$ basis.