Dipolar Interaction - Polar Coordinate

Rewrite the hamiltonian of the dipolar interaction in polar coordinate. Expand the operator to increasing-lowering basis

Solid Echo

• Write out the Solid Echo sequence.
• Show that if add the 3rd spin there will be no refocusing

JB Echo

• Write out the JB echo sequence.
• Show that the magnitude of the dipolar hamiltonian at the end is 1/2 of the magnitization
• Show that if use arbitrary pulse instead of pi/4 pulse, it will give a dipolar state, but not maximum

Lee-Goldberg

Get the hamiltonian of the system by doing averaging transformation

Magic Echo

Show that the following sequence does the same thing as magic echo

Dyson time velocity operation

Show that exp(-i(A+B))t != exp(-iAt)exp(-iBt) unless [A,B]=0.
It is equal to exp(-iAt)T exp(-i integrate[B'(t)]dt) ; B'=exp(iAt)B exp(-iAt), T is Dyson time velocity operator.

WAHUHA Sequence

• Show that H~(1) = 0 => if symmetric sequence H~(odd) = 0
• Show that H~(0)finite pulse != 0, but equal to w1/wD

MREV-8

Show that H~D(0)finite pulse width = 0

BR24, C24

• Show that anti-cyclic H~D(0) = 0
• Show that this is a dipolar decouple pi pulse