Average.m

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Average Hamiltonian theories under Zeeman interaction rotating frame transformations. Syntax:

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

Parameters:

    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)

Note: Krylov-Bogolyubov averging theory as applied to DNP systems is described in detail here:

               http://dx.doi.org/10.1039/C2CP23233B
               http://dx.doi.org/10.1007/s00723-012-0367-0