Bloch equations

In physics and chemistry, specifically in nuclear magnetic resonance (NMR), magnetic resonance imaging (MRI), and electron spin resonance (ESR), the Bloch equations are a set of macroscopic equations that are used to calculate the nuclear magnetization M = (M_x, M_y, M_z) as a function of time when relaxation times T₁ and T₂ are present. These are phenomenological equations that were introduced by Felix Bloch in 1946.^[1] Sometimes they are called the equations of motion of nuclear magnetization. They are analogous to the Maxwell–Bloch equations.