Читать книгу Essential Concepts in MRI - Yang Xia - Страница 40

When both B₀ and B₁(t) are present and perpendicular to each other (B₁ in the transverse plane), we can write down the Hamiltonian in the laboratory frame as

(3.22)

In the rotating frame, the Hamiltonian becomes

(3.23)

At ω = ω₀, we have

(3.24)

Since Ix=12(I++I−), where I₊ and I_- are the raising and lowering operators defined in Appendix A2.4, the time evolution of the spin system corresponds to an inter-conversion of each spin between |1/2> and |–1/2> at a rate of γB₁ (an oscillation).