lecture4_product_op_1

lecture4_product_op_1 - A. S. Edison University of Florida...

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Unformatted text preview: A. S. Edison University of Florida 2009 Todays Lecture 4) Fri, Oct 9: Product operators I (tools to simplify the quantum mechanics) a. RF pulses b. Chemical shift A. S. Edison University of Florida 2009 Weve really just been talking about rotations most of the time! NMR is all rotations. A. S. Edison University of Florida 2009 = 1 Mx Vector representations of Mx, My, and Mz = 1 My = 1 Mz x y z x y z x y z x y z x y z x y z Notice that the coordinate system satisfies the right hand rule. If you point your right thumb along the z-axis, you fingers will close from x to y. A. S. Edison University of Florida 2009 Rotation Matrices - = ) ( ) ( ) ( ) ( 1 ) ( f f f f f Cos Sin Sin Cos Rx - = ) ( ) ( 1 ) ( ) ( ) ( f f f f f Cos Sin Sin Cos Ry - = 1 ) ( ) ( ) ( ) ( ) ( f f f f f Cos Sin Sin Cos Rz These are 3D rotation matrices. When they act on a vector, they rotate the vector around the axis that defines the vector (Rx around x; Ry around y; Rz around z). A. S. Edison University of Florida 2009 What is a rotation?...
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This note was uploaded on 06/07/2011 for the course BCH 6745 taught by Professor Staff during the Spring '08 term at University of Florida.

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lecture4_product_op_1 - A. S. Edison University of Florida...

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