{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

lecture4_product_op_1

# lecture4_product_op_1 - Todays Lecture 4 Fri Oct 9 Product...

This preview shows pages 1–6. Sign up to view the full content.

A. S. Edison University of Florida 2009 Today’s Lecture 4) Fri, Oct 9: Product operators I (tools to simplify the quantum mechanics) a. RF pulses b. Chemical shift

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
A. S. Edison University of Florida 2009 We’ve really just been talking about rotations most of the time! NMR is all rotations.
A. S. Edison University of Florida 2009 = 0 0 1 Mx Vector representations of Mx, My, and Mz = 0 1 0 My = 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.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
A. S. Edison University of Florida 2009 Rotation Matrices - = ) ( ) ( 0 ) ( ) ( 0 0 0 1 ) ( f f f f f Cos Sin Sin Cos Rx - = ) ( 0 ) ( 0 1 0 ) ( 0 ) ( ) ( f f f f f Cos Sin Sin Cos Ry - = 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 2009 What is a rotation? - = ) ( ) ( 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 : = 1 0 0 Mz

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 14

lecture4_product_op_1 - Todays Lecture 4 Fri Oct 9 Product...

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online