# intrep.m

Interaction representation transformation with respect to a specified Hamiltonian to specified order in perturbation theory (https://doi.org/10.1063/1.4928978).

## Contents

## Syntax

Hr=intrep(spin_system,H0,H,T,order)

## Arguments

H0 - the Hamiltonian with respect to which the interaction representation transformation is to be done, typically Zeeman Hamiltonian H - laboratory frame Hamiltonian H0+H1 that is to be transformed into the interaction rep- resentation, typically the full Hamiltonian T - period of the H0 propagator order - perturbation theory order in the rotating frame transformation, this may be inf

## Outputs

Hr - Hamiltonian in the interaction representation

## Examples

See 14N quadrupolar NMR examples (examples/nmr_solids/rframe_nqi_*.m) where the quadrupolar shift is a second order perturbation theory property.

## Notes

This module is called by context functions when the user specifies a numerical rotating frame transformation. It is generally a good idea to do this when your interactions are not much smaller than the Zeeman Hamiltonian, but you are not willing to run the calculation in the laboratory frame.

## See also

dirdiff.m, expmint.m, average.m

*Version 2.2, authors: Ilya Kuprov, David Goodwin*