# average.m

Average Hamiltonian theories under Zeeman interaction rotating frame transformations.

## Contents

## Syntax

H=average(spin_system,Hp,H0,Hm,omega,theory)

## Arguments

Hp - the part of the rotating frame Hamiltonian that has positive frequency under the rotating frame transformation H0 - the part of the rotating frame Hamiltonian that has zero frequency under the rotating frame transformation Hm - the part of the rotating frame Hamiltonian that has negative frequency under the rotating frame transformation omega - the frequency of the rotating frame transformation, rad/s theory - the level of the average Hamiltonian theory: 'ah_first_order' - first order in Waugh theory 'ah_second_order' - second order in Waugh theory 'ah_third_order' - third order in Waugh theory 'matrix_log' - exact algorithm (very expensive, uses dense matrix algebra) 'kb_first_order' - first order in Krylov-Bogolyubov theory (DNP experiments only) 'kb_second_order' - second order in Krylov-Bogolyubov theory (DNP experiments only) 'kb_second_order' - third order in Krylov-Bogolyubov theory (DNP experiments only)

## Outputs

H - average Hamiltonian

## Notes

Krylov-Bogolyubov averging theory as applied to DNP systems is described in detail here in http://dx.doi.org/10.1039/C2CP23233B and http://dx.doi.org/10.1007/s00723-012-0367-0

## See also

rotframe.m, expmint.m, intrep.m

*Version 2.2, authors: Alexander Karabanov, Walter Kockenberger, Ilya Kuprov*