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Unformatted text preview: A. S. Edison University of Florida 2006 Today’s Lecture 6) Mon, Oct 14: Product operators II a. Scalar (J) coupling b. Multiple pulse experiments A. S. Edison University of Florida 2006 Last lecture we discussed rotations of bulk magnetization. r r r r r r r r r r = 1 Mx x x x x x x x x x x = 1 My x x x x x x x x x x = 1 Mz x y z x y z x y z x y z x y z x y z This was the example of a rotation of Mz around the xaxis by an angle φ . The vector went toward the –y axis. . . . . . . . . . . = + + + + + = ) ( ) ( ) ( ) ( 1 ) ( ) ( ) ( ) ( 1 f f f f f f f f Cos Sin Cos Sin Cos Sin Sin Cos A. S. Edison University of Florida 2006 Now we get a bit more complicated… How many states does a spin ½ particle have? 2 (don’t forget 2I+1) How do the 2 quantum states relate to 3D Cartesian space? Different Cartesian orientations arise from a superposition of quantum mechanical states. A. S. Edison University of Florida 2006 Quantum mechanics again r r r r r r = 1 a x x x x x x = 1 1 2 1 x I For a proper treatment of the subject, please see books by Abragam, Ernst et al, Goldman, Farrar, or Cavanagh et al. . . . . . . = 1 b The spin can be in two states: The angular momentum can be represented by: . . . . . . = 2 1 i i I y x x x x x x = 1 1 2 1 z I Pauli spin matrices A. S. Edison University of Florida 2006 Quantum Mechanics Rotations r r r r r r = ) 2 / cos( ) 2 / sin( ) 2 / sin( ) 2 / cos( ) ( q q q q q i i R x QM still involves rotations. Now it is slightly more complicated, so I will just present one case and let the interested students read the complete treatments.interested students read the complete treatments....
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 Spring '08
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 Cartesian Coordinate System, René Descartes, Wolfgang Pauli, spinor

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