Open AccessBloch equations revisited: New analytical solutions for the generalized Bloch equations
Author(s) -
Madhu P. K.,
Kumar Anil
Publication year - 1997
Publication title -
concepts in magnetic resonance
Language(s) - English
Resource type - Journals
eISSN - 1099-0534
pISSN - 1043-7347
DOI - 10.1002/(sici)1099-0534(1997)9:1<1::aid-cmr1>3.0.co;2-2
Subject(s) - bloch equations , component (thermodynamics) , cartesian coordinate system , magnetization , matrix (chemical analysis) , mathematics , state (computer science) , bloch wave , mathematical analysis , physics , statistical physics , quantum mechanics , chemistry , algorithm , geometry , magnetic field , chromatography
The generalized Bloch equations in the rotating frame are solved in Cartesian space by an approach that is different from the earlier Torrey solutions. The solutions are cast into a compact and convenient matrix notation, which paves the way for a direct physical insight and comprehension of the evolution of various magnetization components. The solutions are expressed as a sum of two terms: One describes the decay of the initial state; the other describes the growth of the steady state. The representative trajectories of each component of the above terms plotted separately describe the complete time evolution of each magnetization component. © 1997 John Wiley & Sons, Inc.