1. The problem statement, all variables and given/known data We have spin-1 particle in zero magnetic field. Eigenstates and eigenvalue of operator [itex] \hat S_z [/itex] is [itex] - \hbar |-1> [/itex], [itex] 0 |0> [/itex] and [itex] \hbar |+1> [/itex]. Calculate the first order of splitting which results from the application of a weak magnetic field in the x direction. 2. Relevant equations Hamiltonian is perturbed by [itex] H' = \gamma B \hat S_x = - ( \gamma B/2) (\hat S_+ + \hat S_-)[/itex] 3. The attempt at a solution We have to solve it using degenerate perturbation theory in the basis mentioned, and check it which the basis of eigenvectors of [itex] \hat S_x [/itex]. I am really confused with quantum mechanics, thus would like to know how do we start the question. Is there anyone that can help us by going through step by step how should we go about it and explain it as well?