Please provide detailed answer

Consider a pure spin 1/2 (no orbital degrees of freedom to worry about) placed in a uniform constant magnetic field B in the direction of the Z- axis. The spin is also subjected to a weak "rotating" magnetic field B1(t) = bo (e, cos 21 +ey sin S2t), where ex.y are unit vectors in the directions of X- and Y-axes. Considering the rotating" field as a perturbation, 1. Find the time-dependent spinor describing the quantum state of this spin in the first order of the time-dependent perturbation theory, and compute the expectation values of all three spin components. 2. Assuming that the perturbing field was turned off at time t = T and z-component of the field is measured, find the probabilities of various outcomes. Repeat the same if the x-component is measured. Analyze the obtained results as a function of parameter 27. In all cases assume that initially the spin was in its ground state. Consider a pure spin 1/2 (no orbital degrees of freedom to worry about) placed in a uniform constant magnetic field B in the direction of the Z- axis. The spin is also subjected to a weak "rotating" magnetic field B1(t) = bo (e, cos 21 +ey sin S2t), where ex.y are unit vectors in the directions of X- and Y-axes. Considering the rotating" field as a perturbation, 1. Find the time-dependent spinor describing the quantum state of this spin in the first order of the time-dependent perturbation theory, and compute the expectation values of all three spin components. 2. Assuming that the perturbing field was turned off at time t = T and z-component of the field is measured, find the probabilities of various outcomes. Repeat the same if the x-component is measured. Analyze the obtained results as a function of parameter 27. In all cases assume that initially the spin was in its ground state