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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 ''T''1 and ''T''2 are present. These are phenomenological equations that were introduced by Felix Bloch in 1946.〔F Bloch, ''Nuclear Induction'', Physical Review 70, 460-473 (1946)〕 Sometimes they are called the equations of motion of nuclear magnetization. They are analogous to the Maxwell-Bloch equations. ==Bloch equations in laboratory (stationary) frame of reference== Let M(''t'') = (''Mx''(''t''), ''My''(''t''), ''Mz''(''t'')) be the nuclear magnetization. Then the Bloch equations read: : : : where γ is the gyromagnetic ratio and B(''t'') = (''B''''x''(''t''), ''B''''y''(''t''), ''B''0 + Δ''B''''z''(t)) is the magnetic field experienced by the nuclei. The ''z'' component of the magnetic field B is sometimes composed of two terms: *one, ''B''0, is constant in time, *the other one, Δ''B''''z''(t), may be time dependent. It is present in magnetic resonance imaging and helps with the spatial decoding of the NMR signal. M(''t'') × B(''t'') is the cross product of these two vectors. ''M''0 is the steady state nuclear magnetization (that is, for example, when t → ∞); it is in the ''z'' direction. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Bloch equations」の詳細全文を読む スポンサード リンク
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