Magnetic resonance. A spin-1/2 particle with gyromagnetic ratio Y, at rest in a static magnetic field B0 k̂, precesses at the Larmor frequency ω0=γB0( Example 4.3) . Now we turn on a small transverse radiofrequency (rf) field, Brf[cos(ωt) t̂-sin(ωt) Ĵ], so that the total field is 𝐁=Brfcos (ω t) î-Brfsin (ω t) B0k̂ (a) Construct the 2 ×2 Hamiltonian matrix (Equation 4.158 ) for this system. (b) If χ(t)=( a(t) b(t)) is the spin state at time t, show that ȧ=(i)/(2)(Ω e^i ω t b ω0
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