Abstract
We treat in this effort the problem of time evolution during a time dependent radio-frequency pulse in the First Rotating Frame (FRF) with Fractal Time Derivatives for the Representation of the Schroedinger Equation and Fractal Density Matrix for Like Spins ½. The resultant time evolutions during a Sin-Cos Pulse are compared with the Time Dependence during the Fractal Bloch equations without relaxation solved using Standard Runge Kutta methods.
Highlights
The ability to model spin systems time evolution occurring during radiofrequency (RF) irradiation has increased importance to the expanding use of shaped RF pulses [1,2]
In this effort we extend the theoretical treatment using Fractal Time Derivatives to the case of a Fractal Density Matrix for spin 1⁄2 nuclei
Fractal Density Matrices for spin 1⁄2, and in the Schroedinger Picture, apply it to obtain magnetization profiles valid in the First Rotating frame (FRF) for various values of the fractal coefficient which we compare with the Profiles obtained through numerical solution of the Bloch equations without relaxation defined in the First Rotating Frame (FRF) [9,10,11,12,13]
Summary
The ability to model spin systems time evolution occurring during radiofrequency (RF) irradiation has increased importance to the expanding use of shaped RF pulses [1,2]. In this effort we extend the theoretical treatment using Fractal Time Derivatives to the case of a Fractal Density Matrix for spin 1⁄2 nuclei.
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