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UBC Theses and Dissertations

Application of Green's function technique to paramagnetic resonance Frank, Barry


This thesis contains discussions of a number of points which arose when the author was studying the "paramagnetic resonance line shape problem". The so-called moment method is discussed, and a new derivation of the moments of the line shape function is given. Single-spin operators are introduced which simplify the calculation of these moments. The Green's function technique, as applied to this problem, and the decoupling approximations associated with the technique, are looked at from the point of view of reliability and complexity. As a test of the reliability of any decoupling, a theorem concerning the moments of a line shape arising from such a decoupling is discussed and proved. The Green's function technique is applied to the case of the one-dimensional Ising model with spin ½, where no decoupling of the hierarchy of Green's function equations is necessary. A method of calculating thermal averages for this case, using difference equations, is given.

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