Take the spin Hamiltonian for the hydrogen atom in an external magnetic field B0 in the z direction to be
H^=ℏ22AS^1⋅S^2+ω0S^1z
where ω0=geB0/2mc, with m the mass of the electron. The contribution −μ^2⋅B0 of the proton has been neglected because the mass of the proton is roughly 2000 times larger than the mass of the electron. Determine the energies of this system. Examine your results in the limiting cases A≫ℏω0 and A≪ℏω0 by expanding the energy eigenvalues in a Taylor series or binomial expansion through first nonvanishing order.