Magnetic Resonance Problem (pic 1)

    This problem has time dependence (pic 2)

Time-dependent Ψ? (pic 3)

Plug in to Schrodinger Equation (pic 3)

Solve S.E. with unknown functions. (pic 4,5)
   Plug back into S.E. from matrices    
     ↓
   Nice concise equation system (pic 6)
     ↓ Time derivative of both sides (pic 7)
    Final Solution? Yes, and apply initial conditions.

    Minus sign is switched somewhere in these pictures
    
    