The spin-dependent Hamiltonian of an electron–positron system in the presence of a uniform magnetic field in the z-direction (B=Bk) can be written as
H^=λS^1⋅S^2+(mceB)(S^1z−S^2z),
where λ is a real number and S1 and S2 are the spin operators for the electron and the positron, respectively.
(a) If the spin function of the system is given by ∣21,−21⟩, find the energy eigenvalues and their corresponding eigenvectors.
(b) Repeat (a) in the case where λ=0, but B=0.
(c) Repeat (a) in the case where B=0, but λ=0.