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# lecture5 - Today's Lecture 5 Wed Oct 11 Product operators...

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A. S. Edison University of Florida 2006 Today’s Lecture 5) Wed, Oct 11: Product operators I (tools to simplify the quantum mechanics) a. RF pulses b. Chemical shift

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A. S. Edison University of Florida 2006 We’ve really just been talking about rotations most of the time! NMR is all rotations.
A. S. Edison University of Florida 2006 . . . . . . . . . . = 0 0 1 Mx Vector representations of Mx, My, and Mz . . . . . . . . . . = 0 1 0 My x x x x x x x x x x = 1 0 0 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.

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A. S. Edison University of Florida 2006 Rotation Matrices r r r r r r r r r r - = ) ( ) ( 0 ) ( ) ( 0 0 0 1 ) ( f f f f f Cos Sin Sin Cos Rx x x x x x x x x x x - = ) ( 0 ) ( 0 1 0 ) ( 0 ) ( ) ( f f f f f Cos Sin Sin Cos Ry x x x x x x x x x x - = 1 0 0 0 ) ( ) ( 0 ) ( ) ( ) ( 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 2006 What is a rotation? r r r r r r r r r r - = ) ( ) ( 0 ) ( ) ( 0 0 0 1 ) ( f f f f f Cos Sin Sin Cos Rx Here is an example of a rotation of Mz around the x-axis by an angle φ : .

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lecture5 - Today's Lecture 5 Wed Oct 11 Product operators...

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